theory Employee_DesignModel_UMLPart_generated_generated imports "OCL.UML_Main"   "FOCL.Static"   "FOCL.Generator_dynamic_sequential" begin

(* 1 ************************************ 0 + 0 *)  (* term Floor1_infra.print_infra_enum_synonym *)

(* 2 ************************************ 0 + 1 *)
text \<open>
   \label{ex:Employee-DesignModel-UMLPart-generated-generatedemployee-design:uml} \<close>

(* 3 ************************************ 1 + 1 *)
text \<open>\<close>

(* 4 ************************************ 2 + 1 *)
section \<open>Class Model: Introduction\<close>

(* 5 ************************************ 3 + 1 *)
text \<open>

  For certain concepts like classes and class-types, only a generic
  definition for its resulting semantics can be given. Generic means,
  there is a function outside \HOL that ``compiles'' a concrete,
  closed-world class diagram into a ``theory'' of this data model,
  consisting of a bunch of definitions for classes, accessors, method,
  casts, and tests for actual types, as well as proofs for the
  fundamental properties of these operations in this concrete data
  model. \<close>

(* 6 ************************************ 4 + 1 *)
text \<open>
   Such generic function or ``compiler'' can be implemented in
  Isabelle on the \ML level.  This has been done, for a semantics
  following the open-world assumption, for \UML 2.0
  in~\cite{brucker.ea:extensible:2008-b, brucker:interactive:2007}. In
  this paper, we follow another approach for \UML 2.4: we define the
  concepts of the compilation informally, and present a concrete
  example which is verified in Isabelle/\HOL. \<close>

(* 7 ************************************ 5 + 1 *)
subsection \<open>Outlining the Example\<close>

(* 8 ************************************ 6 + 1 *)
text \<open>
   We are presenting here a ``design-model'' of the (slightly
modified) example Figure 7.3, page 20 of
the \OCL standard~\cite{omg:ocl:2012}. To be precise, this theory contains the formalization of
the data-part covered by the \UML class model (see \autoref{fig:Employee-DesignModel-UMLPart-generated-generatedperson}):\<close>

(* 9 ************************************ 7 + 1 *)
text \<open>\<close>

(* 10 ************************************ 8 + 1 *)
text_raw \<open>

\begin{figure}
  \centering\scalebox{.3}{\includegraphics{figures/person.png}}%
  \caption{A simple \UML class model drawn from Figure 7.3,
  page 20 of~\cite{omg:ocl:2012}. \label{fig:Employee-DesignModel-UMLPart-generated-generatedperson}}
\end{figure}
\<close>

(* 11 ************************************ 9 + 1 *)
text_raw \<open>\<close>

(* 12 ************************************ 10 + 1 *)
text \<open>
   This means that the association (attached to the association class
\inlineocl{EmployeeRanking}) with the association ends \inlineocl+boss+ and \inlineocl+employees+ is implemented
by the attribute  \inlineocl+boss+ and the operation \inlineocl+employees+ (to be discussed in the \OCL part
captured by the subsequent theory).
\<close>

(* 13 ************************************ 11 + 1 *)
section \<open>Class Model: The Construction of the Object Universe\<close>

(* 14 ************************************ 12 + 1 *)
text \<open>
   Our data universe  consists in the concrete class diagram just of node's,
and implicitly of the class object. Each class implies the existence of a class
type defined for the corresponding object representations as follows: \<close>

(* 15 ************************************ 13 + 8 *)  (* term Floor1_infra.print_infra_datatype_class_1 *)
datatype ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "oid" "nat option" "int option" "unit option" "bool option" "oid list list option"
datatype ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "oid list option" "int option"
datatype ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
                        | mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "oid" "unit option" "bool option" "oid list list option"
datatype ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t" "nat option" "int option"
datatype ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t"
                        | mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
                        | mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "oid"
datatype ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y" "unit option" "bool option" "oid list list option"
datatype ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y"
                        | mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t"
                        | mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
                        | mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y "oid"
datatype ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y "ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"

(* 16 ************************************ 21 + 11 *)  (* term Floor1_infra.print_infra_datatype_class_2 *)
datatype ty2\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = mk2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "oid list option" "int option"
datatype ty2oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = mk2oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "oid" "nat option" "int option" "unit option" "bool option" "oid list list option" "ty2\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
datatype ty2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "ty2\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
datatype ty2\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "nat option" "int option" "ty2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t option"
datatype ty2oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = mk2oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "oid" "unit option" "bool option" "oid list list option" "ty2\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t"
datatype ty2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "ty2\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t"
datatype ty2\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "unit option" "bool option" "oid list list option" "ty2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y option"
datatype ty2oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = mk2oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "oid" "ty2\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y"
datatype ty2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "ty2\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y"
datatype ty2\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y "ty2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y option"
datatype ty2oid\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = mk2oid\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y "oid" "ty2\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"

(* 17 ************************************ 32 + 8 *)  (* term Floor1_infra.print_infra_datatype_equiv_2of1 *)
definition "class_ty_ext_equiv_2of1_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = (\<lambda>oid inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d. (\<lambda> (mk2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))) (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y))))"
definition "class_ty_ext_equiv_2of1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = (\<lambda> (mk2oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)) \<Rightarrow> (class_ty_ext_equiv_2of1_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)))"
definition "class_ty_ext_equiv_2of1_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = (\<lambda>oid inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d. (\<lambda> (mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (t)) \<Rightarrow> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((case t of None \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))
    | \<lfloor>(mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))\<rfloor> \<Rightarrow> (case (class_ty_ext_equiv_2of1_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)) of (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))) (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))) (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y))))))) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t))))"
definition "class_ty_ext_equiv_2of1\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = (\<lambda> (mk2oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)) \<Rightarrow> (class_ty_ext_equiv_2of1_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)))"
definition "class_ty_ext_equiv_2of1_aux\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = (\<lambda>oid. (\<lambda> (mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)) \<Rightarrow> (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((case t of None \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid))
    | \<lfloor>(mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t))\<rfloor> \<Rightarrow> (case (class_ty_ext_equiv_2of1_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (t)) of (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)) \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t))))
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)) \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))))) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))))"
definition "class_ty_ext_equiv_2of1\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = (\<lambda> (mk2oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid) (t)) \<Rightarrow> (class_ty_ext_equiv_2of1_aux\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid) (t)))"
definition "class_ty_ext_equiv_2of1_aux\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = (\<lambda>oid. (\<lambda> (mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (t)) \<Rightarrow> (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((case t of None \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid))
    | \<lfloor>(mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t))\<rfloor> \<Rightarrow> (case (class_ty_ext_equiv_2of1_aux\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid) (t)) of (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid))) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid))) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))))
    | (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))
    | (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t))) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t))))))))"
definition "class_ty_ext_equiv_2of1\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = (\<lambda> (mk2oid\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid) (t)) \<Rightarrow> (class_ty_ext_equiv_2of1_aux\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid) (t)))"

(* 18 ************************************ 40 + 12 *)  (* term Floor1_infra.print_infra_datatype_equiv_1of2 *)
definition "class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = (\<lambda> (mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (oid , inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))"
definition "class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (mk2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)))"
definition "class_ty_ext_equiv_1of2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) of (oid , inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (mk2oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid) (inh\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (inh\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (own\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (own\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y))))))))"
definition "class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = (\<lambda> (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (oid , inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)
    | (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (var\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (var\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)))) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) of (oid , var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (oid , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)))"
definition "class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)) \<Rightarrow> (mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) ((case t of (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> None
    | (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (tt)) \<Rightarrow> (case (case tt of (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (var\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (var\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))) of (oid , var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> \<lfloor>(mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (tt))))\<rfloor>)))))"
definition "class_ty_ext_equiv_1of2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t)) of (oid , inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (mk2oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid) (inh\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (inh\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (inh\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (own\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (own\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t))))))))"
definition "class_ty_ext_equiv_1of2_get_oid_inh\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = (\<lambda> (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid)) \<Rightarrow> (oid)
    | (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (var\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (var\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)))) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) of (oid , var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (oid))
    | (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)))) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t)) of (oid , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (oid)))"
definition "class_ty_ext_equiv_1of2_aux\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = (\<lambda> (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) ((case t of (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid)) \<Rightarrow> None
    | (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (tt)) \<Rightarrow> (case (case tt of (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (var\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (var\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))) of (oid , var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> \<lfloor>(mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (\<lfloor>(mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (tt))))\<rfloor>))))\<rfloor>)
    | (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (tt)) \<Rightarrow> (case (case tt of (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)) \<Rightarrow> (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t))) of (oid , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> \<lfloor>(mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (tt))))\<rfloor>)))))"
definition "class_ty_ext_equiv_1of2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y = (\<lambda> (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t)) of (oid) \<Rightarrow> (mk2oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (oid) ((class_ty_ext_equiv_1of2_aux\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t) (own\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (own\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (own\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d))))))))"
definition "class_ty_ext_equiv_1of2_get_oid_inh\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = (\<lambda> (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid)) \<Rightarrow> (oid)
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (var\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (var\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)))) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) of (oid , var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (oid))
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)))) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t)) of (oid , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> (oid))
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t) (var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)))) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t)) of (oid) \<Rightarrow> (oid)))"
definition "class_ty_ext_equiv_1of2_aux\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = (\<lambda> (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (t)) \<Rightarrow> (mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((case t of (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid)) \<Rightarrow> None
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (tt)) \<Rightarrow> (case (case tt of (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (var\<^sub>b\<^sub>o\<^sub>s\<^sub>s) (var\<^sub>s\<^sub>a\<^sub>l\<^sub>a\<^sub>r\<^sub>y)) \<Rightarrow> (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t))) of (oid , var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e , var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> \<lfloor>(mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (\<lfloor>(mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t) (\<lfloor>(mk2\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (tt))))\<rfloor>))))\<rfloor>))))\<rfloor>)
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (tt)) \<Rightarrow> (case (case tt of (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (var\<^sub>w\<^sub>o\<^sub>r\<^sub>m\<^sub>h\<^sub>o\<^sub>l\<^sub>e) (var\<^sub>w\<^sub>e\<^sub>i\<^sub>g\<^sub>h\<^sub>t)) \<Rightarrow> (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t))) of (oid , var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d , var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g , var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) \<Rightarrow> \<lfloor>(mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d) (\<lfloor>(mk2\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((class_ty_ext_equiv_1of2_aux\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (tt))))\<rfloor>))))\<rfloor>)
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (tt)) \<Rightarrow> (case (case tt of (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t) (var\<^sub>s\<^sub>o\<^sub>u\<^sub>n\<^sub>d) (var\<^sub>m\<^sub>o\<^sub>v\<^sub>i\<^sub>n\<^sub>g) (var\<^sub>o\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>_\<^sub>w\<^sub>o\<^sub>r\<^sub>l\<^sub>d)) \<Rightarrow> (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t))) of (oid) \<Rightarrow> \<lfloor>(mk2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((class_ty_ext_equiv_1of2_aux\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (tt))))\<rfloor>)))))"
definition "class_ty_ext_equiv_1of2\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y = (\<lambda> (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (t)) \<Rightarrow> (case (class_ty_ext_equiv_1of2_get_oid_inh\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (t)) of (oid) \<Rightarrow> (mk2oid\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid) ((class_ty_ext_equiv_1of2_aux\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (t))))))))"

(* 19 ************************************ 52 + 1 *)
text \<open>
   Now, we construct a concrete ``universe of OclAny types'' by injection into a
sum type containing the class types. This type of OclAny will be used as instance
for all respective type-variables. \<close>

(* 20 ************************************ 53 + 1 *)  (* term Floor1_infra.print_infra_datatype_universe *)
datatype \<AA> = in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
                        | in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t "ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t"
                        | in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y "ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y"
                        | in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y "ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"

(* 21 ************************************ 54 + 1 *)
text \<open>
   Having fixed the object universe, we can introduce type synonyms that exactly correspond
to \OCL types. Again, we exploit that our representation of \OCL is a ``shallow embedding'' with a
one-to-one correspondance of \OCL-types to types of the meta-language \HOL. \<close>

(* 22 ************************************ 55 + 7 *)  (* term Floor1_infra.print_infra_type_synonym_class *)
type_synonym Void = "\<AA> Void"
type_synonym Boolean = "\<AA> Boolean"
type_synonym Integer = "\<AA> Integer"
type_synonym Real = "\<AA> Real"
type_synonym String = "\<AA> String"
type_synonym '\<alpha> val' = "(\<AA>, '\<alpha>) val"
type_notation val' ("\<cdot>(_)")

(* 23 ************************************ 62 + 4 *)  (* term Floor1_infra.print_infra_type_synonym_class_higher *)
type_synonym Person = "\<langle>\<langle>ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rangle>\<^sub>\<bottom>\<rangle>\<^sub>\<bottom>"
type_synonym Planet = "\<langle>\<langle>ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t\<rangle>\<^sub>\<bottom>\<rangle>\<^sub>\<bottom>"
type_synonym Galaxy = "\<langle>\<langle>ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y\<rangle>\<^sub>\<bottom>\<rangle>\<^sub>\<bottom>"
type_synonym OclAny = "\<langle>\<langle>ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rangle>\<^sub>\<bottom>\<rangle>\<^sub>\<bottom>"

(* 24 ************************************ 66 + 3 *)  (* term Floor1_infra.print_infra_type_synonym_class_rec *)
type_synonym Sequence_Person = "(\<AA>, ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n option option Sequence\<^sub>b\<^sub>a\<^sub>s\<^sub>e) val"
type_synonym Set_Person = "(\<AA>, ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n option option Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) val"
type_synonym Set_Sequence_Planet = "(\<AA>, ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t option option Sequence\<^sub>b\<^sub>a\<^sub>s\<^sub>e Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) val"

(* 25 ************************************ 69 + 0 *)  (* term Floor1_infra.print_infra_enum_syn *)

(* 26 ************************************ 69 + 1 *)
text \<open>
   To reuse key-elements of the library like referential equality, we have
to show that the object universe belongs to the type class ``oclany,'' \ie,
 each class type has to provide a function @{term oid_of} yielding the Object ID (oid) of the object. \<close>

(* 27 ************************************ 70 + 4 *)  (* term Floor1_infra.print_infra_instantiation_class *)
instantiation ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: object
begin
  definition oid_of_ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def : "oid_of = (\<lambda> mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n t _ _ \<Rightarrow> (case t of (mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t) (_) (_) (_) (_) (_)) \<Rightarrow> t))"
  instance ..
end
instantiation ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :: object
begin
  definition oid_of_ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_def : "oid_of = (\<lambda> mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t t _ _ \<Rightarrow> (case t of (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t) (_) (_) (_)) \<Rightarrow> t
    | (mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) \<Rightarrow> (oid_of (t))))"
  instance ..
end
instantiation ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :: object
begin
  definition oid_of_ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_def : "oid_of = (\<lambda> mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y t _ _ _ \<Rightarrow> (case t of (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t)) \<Rightarrow> t
    | (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) \<Rightarrow> (oid_of (t))
    | (mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t)) \<Rightarrow> (oid_of (t))))"
  instance ..
end
instantiation ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: object
begin
  definition oid_of_ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_def : "oid_of = (\<lambda> mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y t \<Rightarrow> (case t of (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (t)) \<Rightarrow> t
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (t)) \<Rightarrow> (oid_of (t))
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (t)) \<Rightarrow> (oid_of (t))
    | (mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (t)) \<Rightarrow> (oid_of (t))))"
  instance ..
end

(* 28 ************************************ 74 + 1 *)  (* term Floor1_infra.print_infra_instantiation_universe *)
instantiation \<AA> :: object
begin
  definition oid_of_\<AA>_def : "oid_of = (\<lambda> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n Person \<Rightarrow> oid_of Person
    | in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t Planet \<Rightarrow> oid_of Planet
    | in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y Galaxy \<Rightarrow> oid_of Galaxy
    | in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y OclAny \<Rightarrow> oid_of OclAny)"
  instance ..
end

(* 29 ************************************ 75 + 1 *)
section \<open>Class Model: Instantiation of the Generic Strict Equality\<close>

(* 30 ************************************ 76 + 1 *)
text \<open>
   We instantiate the referential equality
on @{text "Person"} and @{text "OclAny"} \<close>

(* 31 ************************************ 77 + 4 *)  (* term Floor1_infra.print_instantia_def_strictrefeq *)
overloading StrictRefEq \<equiv> "(StrictRefEq::(\<cdot>Person) \<Rightarrow> _ \<Rightarrow> _)"
begin
  definition StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n : "(x::\<cdot>Person) \<doteq> y \<equiv> StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t x y"
end
overloading StrictRefEq \<equiv> "(StrictRefEq::(\<cdot>Planet) \<Rightarrow> _ \<Rightarrow> _)"
begin
  definition StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t : "(x::\<cdot>Planet) \<doteq> y \<equiv> StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t x y"
end
overloading StrictRefEq \<equiv> "(StrictRefEq::(\<cdot>Galaxy) \<Rightarrow> _ \<Rightarrow> _)"
begin
  definition StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y : "(x::\<cdot>Galaxy) \<doteq> y \<equiv> StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t x y"
end
overloading StrictRefEq \<equiv> "(StrictRefEq::(\<cdot>OclAny) \<Rightarrow> _ \<Rightarrow> _)"
begin
  definition StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y : "(x::\<cdot>OclAny) \<doteq> y \<equiv> StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t x y"
end

(* 32 ************************************ 81 + 1 *)  (* term Floor1_infra.print_instantia_lemmas_strictrefeq *)
lemmas[simp,code_unfold] = StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n
                            StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t
                            StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y
                            StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y

(* 33 ************************************ 82 + 1 *)
text \<open>
   For each Class \emph{C}, we will have a casting operation \inlineocl{.oclAsType($C$)},
   a test on the actual type \inlineocl{.oclIsTypeOf($C$)} as well as its relaxed form
   \inlineocl{.oclIsKindOf($C$)} (corresponding exactly to Java's \verb+instanceof+-operator.
\<close>

(* 34 ************************************ 83 + 1 *)
text \<open>
   Thus, since we have two class-types in our concrete class hierarchy, we have
two operations to declare and to provide two overloading definitions for the two static types.
\<close>

(* 35 ************************************ 84 + 1 *)
section \<open>Class Model: OclAsType\<close>

(* 36 ************************************ 85 + 1 *)
subsection \<open>Definition\<close>

(* 37 ************************************ 86 + 4 *)  (* term Floor1_astype.print_astype_consts *)
consts OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> \<cdot>Person" ("(_) .oclAsType'(Person')")
consts OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :: "'\<alpha> \<Rightarrow> \<cdot>Planet" ("(_) .oclAsType'(Planet')")
consts OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :: "'\<alpha> \<Rightarrow> \<cdot>Galaxy" ("(_) .oclAsType'(Galaxy')")
consts OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> \<cdot>OclAny" ("(_) .oclAsType'(OclAny')")

(* 38 ************************************ 90 + 16 *)  (* term Floor1_astype.print_astype_class *)
overloading OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person : "(x::\<cdot>Person) .oclAsType(Person) \<equiv> x"
end
overloading OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet : "(x::\<cdot>Planet) .oclAsType(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>Person\<rfloor>\<rfloor>
    | _ \<Rightarrow> (invalid (\<tau>))))"
end
overloading OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy : "(x::\<cdot>Galaxy) .oclAsType(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (_) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>Person\<rfloor>\<rfloor>
    | _ \<Rightarrow> (invalid (\<tau>))))"
end
overloading OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny : "(x::\<cdot>OclAny) .oclAsType(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))))\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>Person\<rfloor>\<rfloor>
    | _ \<Rightarrow> (invalid (\<tau>))))"
end
overloading OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet : "(x::\<cdot>Planet) .oclAsType(Planet) \<equiv> x"
end
overloading OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy : "(x::\<cdot>Galaxy) .oclAsType(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))) (_) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>Planet\<rfloor>\<rfloor>
    | _ \<Rightarrow> (invalid (\<tau>))))"
end
overloading OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny : "(x::\<cdot>OclAny) .oclAsType(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))))\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>Planet\<rfloor>\<rfloor>
    | _ \<Rightarrow> (invalid (\<tau>))))"
end
overloading OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person : "(x::\<cdot>Person) .oclAsType(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>Person\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>(mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (None) (None))\<rfloor>\<rfloor>))"
end
overloading OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy : "(x::\<cdot>Galaxy) .oclAsType(Galaxy) \<equiv> x"
end
overloading OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny : "(x::\<cdot>OclAny) .oclAsType(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy))))\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>Galaxy\<rfloor>\<rfloor>
    | _ \<Rightarrow> (invalid (\<tau>))))"
end
overloading OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person : "(x::\<cdot>Person) .oclAsType(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>Person\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (None) (None) (None))\<rfloor>\<rfloor>))"
end
overloading OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet : "(x::\<cdot>Planet) .oclAsType(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>Planet\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))) (None) (None) (None))\<rfloor>\<rfloor>))"
end
overloading OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny : "(x::\<cdot>OclAny) .oclAsType(OclAny) \<equiv> x"
end
overloading OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person : "(x::\<cdot>Person) .oclAsType(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>Person\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))))\<rfloor>\<rfloor>))"
end
overloading OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet : "(x::\<cdot>Planet) .oclAsType(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>Planet\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))))\<rfloor>\<rfloor>))"
end
overloading OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy : "(x::\<cdot>Galaxy) .oclAsType(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (null (\<tau>))
    | \<lfloor>\<lfloor>Galaxy\<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy))))\<rfloor>\<rfloor>))"
end

(* 39 ************************************ 106 + 4 *)  (* term Floor1_astype.print_astype_from_universe *)
definition "OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA> = (\<lambda> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> \<lfloor>Person\<rfloor>
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (_) (_)))) \<Rightarrow> \<lfloor>Person\<rfloor>
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (_) (_) (_)))) \<Rightarrow> \<lfloor>Person\<rfloor>
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)))))) \<Rightarrow> \<lfloor>Person\<rfloor>
    | _ \<Rightarrow> None)"
definition "OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA> = (\<lambda> (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> \<lfloor>Planet\<rfloor>
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))) (_) (_) (_)))) \<Rightarrow> \<lfloor>Planet\<rfloor>
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)))))) \<Rightarrow> \<lfloor>Planet\<rfloor>
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> \<lfloor>(mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (None) (None))\<rfloor>
    | _ \<Rightarrow> None)"
definition "OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA> = (\<lambda> (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> \<lfloor>Galaxy\<rfloor>
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)))))) \<Rightarrow> \<lfloor>Galaxy\<rfloor>
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> \<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))) (None) (None) (None))\<rfloor>
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> \<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))) (None) (None) (None))\<rfloor>
    | _ \<Rightarrow> None)"
definition "OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA> = Some o (\<lambda> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> OclAny
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person))))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet))))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)))))"

(* 40 ************************************ 110 + 1 *)  (* term Floor1_astype.print_astype_lemmas_id *)
lemmas[simp,code_unfold] = OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny

(* 41 ************************************ 111 + 1 *)
subsection \<open>Context Passing\<close>

(* 42 ************************************ 112 + 64 *)  (* term Floor1_astype.print_astype_lemma_cp *)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclAsType(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclAsType(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclAsType(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclAsType(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclAsType(OclAny)))))"
by(rule cpI1, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclAsType(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclAsType(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclAsType(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclAsType(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclAsType(Galaxy)))))"
by(rule cpI1, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclAsType(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclAsType(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclAsType(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclAsType(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclAsType(Planet)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclAsType(Person)))))"
by(rule cpI1, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclAsType(Person)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclAsType(Person)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclAsType(Person)))))"
by(rule cpI1, simp)
lemma cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclAsType(Person)))))"
by(rule cpI1, simp)

(* 43 ************************************ 176 + 1 *)  (* term Floor1_astype.print_astype_lemmas_cp *)
lemmas[simp,code_unfold] = cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person
                            cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person
                            cp_OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person
                            cp_OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person
                            cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person

(* 44 ************************************ 177 + 1 *)
subsection \<open>Execution with Invalid or Null as Argument\<close>

(* 45 ************************************ 178 + 32 *)  (* term Floor1_astype.print_astype_lemma_strict *)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclAsType(OclAny)) = invalid"
by(simp)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclAsType(OclAny)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy bot_option_def invalid_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid : "((invalid::\<cdot>Planet) .oclAsType(OclAny)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet bot_option_def invalid_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid : "((invalid::\<cdot>Person) .oclAsType(OclAny)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person bot_option_def invalid_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null : "((null::\<cdot>OclAny) .oclAsType(OclAny)) = null"
by(simp)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null : "((null::\<cdot>Galaxy) .oclAsType(OclAny)) = null"
by(rule ext, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null : "((null::\<cdot>Planet) .oclAsType(OclAny)) = null"
by(rule ext, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null : "((null::\<cdot>Person) .oclAsType(OclAny)) = null"
by(rule ext, simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclAsType(Galaxy)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny bot_option_def invalid_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclAsType(Galaxy)) = invalid"
by(simp)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid : "((invalid::\<cdot>Planet) .oclAsType(Galaxy)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet bot_option_def invalid_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid : "((invalid::\<cdot>Person) .oclAsType(Galaxy)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person bot_option_def invalid_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null : "((null::\<cdot>OclAny) .oclAsType(Galaxy)) = null"
by(rule ext, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null : "((null::\<cdot>Galaxy) .oclAsType(Galaxy)) = null"
by(simp)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null : "((null::\<cdot>Planet) .oclAsType(Galaxy)) = null"
by(rule ext, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null : "((null::\<cdot>Person) .oclAsType(Galaxy)) = null"
by(rule ext, simp add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclAsType(Planet)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny bot_option_def invalid_def)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclAsType(Planet)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy bot_option_def invalid_def)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid : "((invalid::\<cdot>Planet) .oclAsType(Planet)) = invalid"
by(simp)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid : "((invalid::\<cdot>Person) .oclAsType(Planet)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person bot_option_def invalid_def)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null : "((null::\<cdot>OclAny) .oclAsType(Planet)) = null"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null : "((null::\<cdot>Galaxy) .oclAsType(Planet)) = null"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null : "((null::\<cdot>Planet) .oclAsType(Planet)) = null"
by(simp)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null : "((null::\<cdot>Person) .oclAsType(Planet)) = null"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclAsType(Person)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny bot_option_def invalid_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclAsType(Person)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy bot_option_def invalid_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid : "((invalid::\<cdot>Planet) .oclAsType(Person)) = invalid"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet bot_option_def invalid_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid : "((invalid::\<cdot>Person) .oclAsType(Person)) = invalid"
by(simp)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null : "((null::\<cdot>OclAny) .oclAsType(Person)) = null"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null : "((null::\<cdot>Galaxy) .oclAsType(Person)) = null"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null : "((null::\<cdot>Planet) .oclAsType(Person)) = null"
by(rule ext, simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet bot_option_def null_fun_def null_option_def)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null : "((null::\<cdot>Person) .oclAsType(Person)) = null"
by(simp)

(* 46 ************************************ 210 + 1 *)  (* term Floor1_astype.print_astype_lemmas_strict *)
lemmas[simp,code_unfold] = OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null

(* 47 ************************************ 211 + 1 *)
subsection \<open>Validity and Definedness Properties\<close>

(* 48 ************************************ 212 + 6 *)  (* term Floor1_astype.print_astype_defined *)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclAsType(Planet)))"
  using isdef
by(auto simp: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person foundation16 null_option_def bot_option_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclAsType(Galaxy)))"
  using isdef
by(auto simp: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person foundation16 null_option_def bot_option_def)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclAsType(Galaxy)))"
  using isdef
by(auto simp: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet foundation16 null_option_def bot_option_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclAsType(OclAny)))"
  using isdef
by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person foundation16 null_option_def bot_option_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclAsType(OclAny)))"
  using isdef
by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet foundation16 null_option_def bot_option_def)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclAsType(OclAny)))"
  using isdef
by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy foundation16 null_option_def bot_option_def)

(* 49 ************************************ 218 + 1 *)
subsection \<open>Up Down Casting\<close>

(* 50 ************************************ 219 + 6 *)  (* term Floor1_astype.print_astype_up_d_cast0 *)
lemma up\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast0 :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (((X::\<cdot>Person) .oclAsType(Planet)) .oclAsType(Person)) \<triangleq> X"
  using isdef
by(auto simp: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast0 :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (((X::\<cdot>Person) .oclAsType(Galaxy)) .oclAsType(Person)) \<triangleq> X"
  using isdef
by(auto simp: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast0 :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (((X::\<cdot>Person) .oclAsType(OclAny)) .oclAsType(Person)) \<triangleq> X"
  using isdef
by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast0 :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (((X::\<cdot>Planet) .oclAsType(Galaxy)) .oclAsType(Planet)) \<triangleq> X"
  using isdef
by(auto simp: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
lemma up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast0 :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (((X::\<cdot>Planet) .oclAsType(OclAny)) .oclAsType(Planet)) \<triangleq> X"
  using isdef
by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
lemma up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_cast0 :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (((X::\<cdot>Galaxy) .oclAsType(OclAny)) .oclAsType(Galaxy)) \<triangleq> X"
  using isdef
by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)

(* 51 ************************************ 225 + 6 *)  (* term Floor1_astype.print_astype_up_d_cast *)
lemma up\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast :
shows "(((X::\<cdot>Person) .oclAsType(Planet)) .oclAsType(Person)) = X"
  apply(rule ext, rename_tac \<tau>)
  apply(rule foundation22[THEN iffD1])
  apply(case_tac "\<tau> \<Turnstile> (\<delta> (X))", simp add: up\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast0)
  apply(simp add: defined_split, elim disjE)
  apply((erule StrongEq_L_subst2_rev, simp, simp)+)
done
lemma up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast :
shows "(((X::\<cdot>Person) .oclAsType(Galaxy)) .oclAsType(Person)) = X"
  apply(rule ext, rename_tac \<tau>)
  apply(rule foundation22[THEN iffD1])
  apply(case_tac "\<tau> \<Turnstile> (\<delta> (X))", simp add: up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast0)
  apply(simp add: defined_split, elim disjE)
  apply((erule StrongEq_L_subst2_rev, simp, simp)+)
done
lemma up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast :
shows "(((X::\<cdot>Person) .oclAsType(OclAny)) .oclAsType(Person)) = X"
  apply(rule ext, rename_tac \<tau>)
  apply(rule foundation22[THEN iffD1])
  apply(case_tac "\<tau> \<Turnstile> (\<delta> (X))", simp add: up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast0)
  apply(simp add: defined_split, elim disjE)
  apply((erule StrongEq_L_subst2_rev, simp, simp)+)
done
lemma up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast :
shows "(((X::\<cdot>Planet) .oclAsType(Galaxy)) .oclAsType(Planet)) = X"
  apply(rule ext, rename_tac \<tau>)
  apply(rule foundation22[THEN iffD1])
  apply(case_tac "\<tau> \<Turnstile> (\<delta> (X))", simp add: up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast0)
  apply(simp add: defined_split, elim disjE)
  apply((erule StrongEq_L_subst2_rev, simp, simp)+)
done
lemma up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast :
shows "(((X::\<cdot>Planet) .oclAsType(OclAny)) .oclAsType(Planet)) = X"
  apply(rule ext, rename_tac \<tau>)
  apply(rule foundation22[THEN iffD1])
  apply(case_tac "\<tau> \<Turnstile> (\<delta> (X))", simp add: up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast0)
  apply(simp add: defined_split, elim disjE)
  apply((erule StrongEq_L_subst2_rev, simp, simp)+)
done
lemma up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_cast :
shows "(((X::\<cdot>Galaxy) .oclAsType(OclAny)) .oclAsType(Galaxy)) = X"
  apply(rule ext, rename_tac \<tau>)
  apply(rule foundation22[THEN iffD1])
  apply(case_tac "\<tau> \<Turnstile> (\<delta> (X))", simp add: up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_cast0)
  apply(simp add: defined_split, elim disjE)
  apply((erule StrongEq_L_subst2_rev, simp, simp)+)
done

(* 52 ************************************ 231 + 6 *)  (* term Floor1_astype.print_astype_d_up_cast *)
lemma down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_up\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast :
assumes def_X: "X = ((Y::\<cdot>Person) .oclAsType(Planet))"
shows "(\<tau> \<Turnstile> ((not ((\<upsilon> (X)))) or ((X .oclAsType(Person)) .oclAsType(Planet)) \<doteq> X))"
  apply(case_tac "(\<tau> \<Turnstile> ((not ((\<upsilon> (X))))))", rule foundation25, simp)
by(rule foundation25', simp add: def_X up\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_sym)
lemma down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_cast :
assumes def_X: "X = ((Y::\<cdot>Person) .oclAsType(Galaxy))"
shows "(\<tau> \<Turnstile> ((not ((\<upsilon> (X)))) or ((X .oclAsType(Person)) .oclAsType(Galaxy)) \<doteq> X))"
  apply(case_tac "(\<tau> \<Turnstile> ((not ((\<upsilon> (X))))))", rule foundation25, simp)
by(rule foundation25', simp add: def_X up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_sym)
lemma down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_cast :
assumes def_X: "X = ((Y::\<cdot>Person) .oclAsType(OclAny))"
shows "(\<tau> \<Turnstile> ((not ((\<upsilon> (X)))) or ((X .oclAsType(Person)) .oclAsType(OclAny)) \<doteq> X))"
  apply(case_tac "(\<tau> \<Turnstile> ((not ((\<upsilon> (X))))))", rule foundation25, simp)
by(rule foundation25', simp add: def_X up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_cast StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_sym)
lemma down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_cast :
assumes def_X: "X = ((Y::\<cdot>Planet) .oclAsType(Galaxy))"
shows "(\<tau> \<Turnstile> ((not ((\<upsilon> (X)))) or ((X .oclAsType(Planet)) .oclAsType(Galaxy)) \<doteq> X))"
  apply(case_tac "(\<tau> \<Turnstile> ((not ((\<upsilon> (X))))))", rule foundation25, simp)
by(rule foundation25', simp add: def_X up\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_sym)
lemma down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_cast :
assumes def_X: "X = ((Y::\<cdot>Planet) .oclAsType(OclAny))"
shows "(\<tau> \<Turnstile> ((not ((\<upsilon> (X)))) or ((X .oclAsType(Planet)) .oclAsType(OclAny)) \<doteq> X))"
  apply(case_tac "(\<tau> \<Turnstile> ((not ((\<upsilon> (X))))))", rule foundation25, simp)
by(rule foundation25', simp add: def_X up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_cast StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_sym)
lemma down\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_cast :
assumes def_X: "X = ((Y::\<cdot>Galaxy) .oclAsType(OclAny))"
shows "(\<tau> \<Turnstile> ((not ((\<upsilon> (X)))) or ((X .oclAsType(Galaxy)) .oclAsType(OclAny)) \<doteq> X))"
  apply(case_tac "(\<tau> \<Turnstile> ((not ((\<upsilon> (X))))))", rule foundation25, simp)
by(rule foundation25', simp add: def_X up\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_down\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_cast StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_sym)

(* 53 ************************************ 237 + 1 *)
subsection \<open>Const\<close>

(* 54 ************************************ 238 + 16 *)  (* term Floor1_astype.print_astype_lemma_const *)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_const : "(const ((X::\<cdot>OclAny))) \<Longrightarrow> (const (X .oclAsType(OclAny)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_const : "(const ((X::\<cdot>Galaxy))) \<Longrightarrow> (const (X .oclAsType(OclAny)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_const : "(const ((X::\<cdot>Planet))) \<Longrightarrow> (const (X .oclAsType(OclAny)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_const : "(const ((X::\<cdot>Person))) \<Longrightarrow> (const (X .oclAsType(OclAny)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_const : "(const ((X::\<cdot>OclAny))) \<Longrightarrow> (const (X .oclAsType(Galaxy)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_const : "(const ((X::\<cdot>Galaxy))) \<Longrightarrow> (const (X .oclAsType(Galaxy)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_const : "(const ((X::\<cdot>Planet))) \<Longrightarrow> (const (X .oclAsType(Galaxy)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_const : "(const ((X::\<cdot>Person))) \<Longrightarrow> (const (X .oclAsType(Galaxy)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_const : "(const ((X::\<cdot>OclAny))) \<Longrightarrow> (const (X .oclAsType(Planet)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_const : "(const ((X::\<cdot>Galaxy))) \<Longrightarrow> (const (X .oclAsType(Planet)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_const : "(const ((X::\<cdot>Planet))) \<Longrightarrow> (const (X .oclAsType(Planet)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_const : "(const ((X::\<cdot>Person))) \<Longrightarrow> (const (X .oclAsType(Planet)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_const : "(const ((X::\<cdot>OclAny))) \<Longrightarrow> (const (X .oclAsType(Person)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_const : "(const ((X::\<cdot>Galaxy))) \<Longrightarrow> (const (X .oclAsType(Person)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_const : "(const ((X::\<cdot>Planet))) \<Longrightarrow> (const (X .oclAsType(Person)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_const : "(const ((X::\<cdot>Person))) \<Longrightarrow> (const (X .oclAsType(Person)))"
by(simp add: const_def, (metis (no_types) OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person prod.collapse bot_option_def invalid_def null_fun_def null_option_def)?)

(* 55 ************************************ 254 + 1 *)  (* term Floor1_astype.print_astype_lemmas_const *)
lemmas[simp,code_unfold] = OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_const
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_const
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_const
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_const
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_const
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_const
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_const
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_const
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_const
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_const
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_const
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_const
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_const
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_const
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_const
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_const

(* 56 ************************************ 255 + 1 *)
section \<open>Class Model: OclIsTypeOf\<close>

(* 57 ************************************ 256 + 1 *)
subsection \<open>Definition\<close>

(* 58 ************************************ 257 + 4 *)  (* term Floor1_istypeof.print_istypeof_consts *)
consts OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsTypeOf'(Person')")
consts OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsTypeOf'(Planet')")
consts OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsTypeOf'(Galaxy')")
consts OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsTypeOf'(OclAny')")

(* 59 ************************************ 261 + 16 *)  (* term Floor1_istypeof.print_istypeof_class *)
overloading OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person : "(x::\<cdot>Person) .oclIsTypeOf(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (_) (_) (_))) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet : "(x::\<cdot>Planet) .oclIsTypeOf(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_))) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy : "(x::\<cdot>Galaxy) .oclIsTypeOf(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_))) (_) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny : "(x::\<cdot>OclAny) .oclIsTypeOf(Person) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_))))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet : "(x::\<cdot>Planet) .oclIsTypeOf(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (_) (_))) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy : "(x::\<cdot>Galaxy) .oclIsTypeOf(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_))) (_) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny : "(x::\<cdot>OclAny) .oclIsTypeOf(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_))))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person : "(x::\<cdot>Person) .oclIsTypeOf(Planet) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy : "(x::\<cdot>Galaxy) .oclIsTypeOf(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_))) (_) (_) (_))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny : "(x::\<cdot>OclAny) .oclIsTypeOf(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_))))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person : "(x::\<cdot>Person) .oclIsTypeOf(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet : "(x::\<cdot>Planet) .oclIsTypeOf(Galaxy) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny : "(x::\<cdot>OclAny) .oclIsTypeOf(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | \<lfloor>\<lfloor>(mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (_))))\<rfloor>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person : "(x::\<cdot>Person) .oclIsTypeOf(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet : "(x::\<cdot>Planet) .oclIsTypeOf(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end
overloading OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy : "(x::\<cdot>Galaxy) .oclIsTypeOf(OclAny) \<equiv> (\<lambda>\<tau>. (case (x (\<tau>)) of \<bottom> \<Rightarrow> (invalid (\<tau>))
    | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> (true (\<tau>))
    | _ \<Rightarrow> (false (\<tau>))))"
end

(* 60 ************************************ 277 + 4 *)  (* term Floor1_istypeof.print_istypeof_from_universe *)
definition "OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA> = (\<lambda> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsTypeOf(Person))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsTypeOf(Person))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsTypeOf(Person))
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsTypeOf(Person)))"
definition "OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA> = (\<lambda> (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsTypeOf(Planet))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsTypeOf(Planet))
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsTypeOf(Planet))
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsTypeOf(Planet)))"
definition "OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA> = (\<lambda> (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsTypeOf(Galaxy))
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsTypeOf(Galaxy))
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsTypeOf(Galaxy))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsTypeOf(Galaxy)))"
definition "OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA> = (\<lambda> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsTypeOf(OclAny))
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsTypeOf(OclAny))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsTypeOf(OclAny))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))"

(* 61 ************************************ 281 + 1 *)  (* term Floor1_istypeof.print_istypeof_lemmas_id *)
lemmas[simp,code_unfold] = OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny

(* 62 ************************************ 282 + 1 *)
subsection \<open>Context Passing\<close>

(* 63 ************************************ 283 + 64 *)  (* term Floor1_istypeof.print_istypeof_lemma_cp *)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsTypeOf(OclAny)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsTypeOf(Galaxy)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsTypeOf(Planet)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp)
lemma cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsTypeOf(Person)))))"
by(rule cpI1, simp)

(* 64 ************************************ 347 + 1 *)  (* term Floor1_istypeof.print_istypeof_lemmas_cp *)
lemmas[simp,code_unfold] = cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person
                            cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person
                            cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person
                            cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person

(* 65 ************************************ 348 + 1 *)
subsection \<open>Execution with Invalid or Null as Argument\<close>

(* 66 ************************************ 349 + 32 *)  (* term Floor1_istypeof.print_istypeof_lemma_strict *)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsTypeOf(OclAny)) = invalid"
by(rule ext, simp add: bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsTypeOf(OclAny)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsTypeOf(OclAny)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid : "((invalid::\<cdot>Person) .oclIsTypeOf(OclAny)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null : "((null::\<cdot>OclAny) .oclIsTypeOf(OclAny)) = true"
by(rule ext, simp add: bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsTypeOf(OclAny)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null : "((null::\<cdot>Planet) .oclIsTypeOf(OclAny)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null : "((null::\<cdot>Person) .oclIsTypeOf(OclAny)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsTypeOf(Galaxy)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)) = invalid"
by(rule ext, simp add: bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsTypeOf(Galaxy)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid : "((invalid::\<cdot>Person) .oclIsTypeOf(Galaxy)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null : "((null::\<cdot>OclAny) .oclIsTypeOf(Galaxy)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)) = true"
by(rule ext, simp add: bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null : "((null::\<cdot>Planet) .oclIsTypeOf(Galaxy)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null : "((null::\<cdot>Person) .oclIsTypeOf(Galaxy)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsTypeOf(Planet)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsTypeOf(Planet)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsTypeOf(Planet)) = invalid"
by(rule ext, simp add: bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid : "((invalid::\<cdot>Person) .oclIsTypeOf(Planet)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null : "((null::\<cdot>OclAny) .oclIsTypeOf(Planet)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsTypeOf(Planet)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null : "((null::\<cdot>Planet) .oclIsTypeOf(Planet)) = true"
by(rule ext, simp add: bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null : "((null::\<cdot>Person) .oclIsTypeOf(Planet)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsTypeOf(Person)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsTypeOf(Person)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsTypeOf(Person)) = invalid"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid : "((invalid::\<cdot>Person) .oclIsTypeOf(Person)) = invalid"
by(rule ext, simp add: bot_option_def invalid_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null : "((null::\<cdot>OclAny) .oclIsTypeOf(Person)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsTypeOf(Person)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null : "((null::\<cdot>Planet) .oclIsTypeOf(Person)) = true"
by(rule ext, simp add: OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet bot_option_def null_fun_def null_option_def)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null : "((null::\<cdot>Person) .oclIsTypeOf(Person)) = true"
by(rule ext, simp add: bot_option_def null_fun_def null_option_def)

(* 67 ************************************ 381 + 1 *)  (* term Floor1_istypeof.print_istypeof_lemmas_strict *)
lemmas[simp,code_unfold] = OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null
                            OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null
                            OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null
                            OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null
                            OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null

(* 68 ************************************ 382 + 1 *)
subsection \<open>Validity and Definedness Properties\<close>

(* 69 ************************************ 383 + 16 *)  (* term Floor1_istypeof.print_istypeof_defined *)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(Person)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(Person)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(Person)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy split: option.split ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(Person)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny split: option.split ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(Planet)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(Planet)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy split: option.split ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(Planet)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny split: option.split ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(Planet)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy split: option.split ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny split: option.split ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(Galaxy)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(Galaxy)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny split: option.split ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(OclAny)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(OclAny)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))"
  apply(insert isdef[simplified foundation18'], simp only: OclValid_def, subst cp_defined)
by(auto simp: cp_defined[symmetric ] bot_option_def OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy split: option.split ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)

(* 70 ************************************ 399 + 16 *)  (* term Floor1_istypeof.print_istypeof_defined' *)
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(Person)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(Person)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(Person)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(Person)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(Planet)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(Planet)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(Planet)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(Planet)))"
by(rule OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)))"
by(rule OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))"
by(rule OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(Galaxy)))"
by(rule OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(Galaxy)))"
by(rule OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny)))"
by(rule OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsTypeOf(OclAny)))"
by(rule OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsTypeOf(OclAny)))"
by(rule OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsTypeOf(OclAny)))"
by(rule OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined[OF isdef[THEN foundation20]])

(* 71 ************************************ 415 + 1 *)
subsection \<open>Up Down Casting\<close>

(* 72 ************************************ 416 + 6 *)  (* term Floor1_istypeof.print_istypeof_up_larger *)
lemma actualType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsTypeOf(Planet)) \<triangleq> false"
  using isdef
by(auto simp: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person foundation22 foundation16 null_option_def bot_option_def)
lemma actualType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsTypeOf(Galaxy)) \<triangleq> false"
  using isdef
by(auto simp: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person foundation22 foundation16 null_option_def bot_option_def)
lemma actualType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsTypeOf(OclAny)) \<triangleq> false"
  using isdef
by(auto simp: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person foundation22 foundation16 null_option_def bot_option_def)
lemma actualType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsTypeOf(Galaxy)) \<triangleq> false"
  using isdef
by(auto simp: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet foundation22 foundation16 null_option_def bot_option_def)
lemma actualType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsTypeOf(OclAny)) \<triangleq> false"
  using isdef
by(auto simp: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet foundation22 foundation16 null_option_def bot_option_def)
lemma actualType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_larger_staticType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(OclAny)) \<triangleq> false"
  using isdef
by(auto simp: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy foundation22 foundation16 null_option_def bot_option_def)

(* 73 ************************************ 422 + 10 *)  (* term Floor1_istypeof.print_istypeof_up_d_cast *)
lemma down_cast_type\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_Planet_to_Person :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsTypeOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
by(simp add: OclValid_def false_def true_def)
lemma down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_Galaxy_to_Person :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
by(simp add: OclValid_def false_def true_def)
lemma down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Person :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
by(simp add: OclValid_def false_def true_def)
lemma down_cast_type\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_Galaxy_to_Person :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
by(simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy OclValid_def false_def true_def)
lemma down_cast_type\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_OclAny_to_Person :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
by(simp add: OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny OclValid_def false_def true_def)
lemma down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Person :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
by(simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny OclValid_def false_def true_def)
lemma down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_Galaxy_to_Planet :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Planet)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
by(simp add: OclValid_def false_def true_def)
lemma down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Planet :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Planet)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
by(simp add: OclValid_def false_def true_def)
lemma down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Planet :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Planet)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
by(simp add: OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny OclValid_def false_def true_def)
lemma down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Galaxy :
assumes istyp: "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Galaxy)) \<triangleq> invalid"
  using istyp isdef
  apply(auto simp: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny foundation22 foundation16 null_option_def bot_option_def split: ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split)
by(simp add: OclValid_def false_def true_def)

(* 74 ************************************ 432 + 1 *)
subsection \<open>Const\<close>

(* 75 ************************************ 433 + 1 *)
section \<open>Class Model: OclIsKindOf\<close>

(* 76 ************************************ 434 + 1 *)
subsection \<open>Definition\<close>

(* 77 ************************************ 435 + 4 *)  (* term Floor1_iskindof.print_iskindof_consts *)
consts OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsKindOf'(Person')")
consts OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsKindOf'(Planet')")
consts OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsKindOf'(Galaxy')")
consts OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_) .oclIsKindOf'(OclAny')")

(* 78 ************************************ 439 + 16 *)  (* term Floor1_iskindof.print_iskindof_class *)
overloading OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person : "(x::\<cdot>Person) .oclIsKindOf(Person) \<equiv> (x .oclIsTypeOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet : "(x::\<cdot>Planet) .oclIsKindOf(Person) \<equiv> (x .oclIsTypeOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy : "(x::\<cdot>Galaxy) .oclIsKindOf(Person) \<equiv> (x .oclIsTypeOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "(OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny : "(x::\<cdot>OclAny) .oclIsKindOf(Person) \<equiv> (x .oclIsTypeOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet : "(x::\<cdot>Planet) .oclIsKindOf(Planet) \<equiv> (x .oclIsTypeOf(Planet)) or (x .oclIsKindOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy : "(x::\<cdot>Galaxy) .oclIsKindOf(Planet) \<equiv> (x .oclIsTypeOf(Planet)) or (x .oclIsKindOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny : "(x::\<cdot>OclAny) .oclIsKindOf(Planet) \<equiv> (x .oclIsTypeOf(Planet)) or (x .oclIsKindOf(Person))"
end
overloading OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t \<equiv> "(OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person : "(x::\<cdot>Person) .oclIsKindOf(Planet) \<equiv> (x .oclIsTypeOf(Planet)) or (x .oclIsKindOf(Person))"
end
overloading OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy : "(x::\<cdot>Galaxy) .oclIsKindOf(Galaxy) \<equiv> (x .oclIsTypeOf(Galaxy)) or (x .oclIsKindOf(Planet))"
end
overloading OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny : "(x::\<cdot>OclAny) .oclIsKindOf(Galaxy) \<equiv> (x .oclIsTypeOf(Galaxy)) or (x .oclIsKindOf(Planet))"
end
overloading OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person : "(x::\<cdot>Person) .oclIsKindOf(Galaxy) \<equiv> (x .oclIsTypeOf(Galaxy)) or (x .oclIsKindOf(Planet))"
end
overloading OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y \<equiv> "(OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet : "(x::\<cdot>Planet) .oclIsKindOf(Galaxy) \<equiv> (x .oclIsTypeOf(Galaxy)) or (x .oclIsKindOf(Planet))"
end
overloading OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny : "(x::\<cdot>OclAny) .oclIsKindOf(OclAny) \<equiv> (x .oclIsTypeOf(OclAny)) or (x .oclIsKindOf(Galaxy))"
end
overloading OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person : "(x::\<cdot>Person) .oclIsKindOf(OclAny) \<equiv> (x .oclIsTypeOf(OclAny)) or (x .oclIsKindOf(Galaxy))"
end
overloading OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet : "(x::\<cdot>Planet) .oclIsKindOf(OclAny) \<equiv> (x .oclIsTypeOf(OclAny)) or (x .oclIsKindOf(Galaxy))"
end
overloading OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y \<equiv> "(OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy : "(x::\<cdot>Galaxy) .oclIsKindOf(OclAny) \<equiv> (x .oclIsTypeOf(OclAny)) or (x .oclIsKindOf(Galaxy))"
end

(* 79 ************************************ 455 + 4 *)  (* term Floor1_iskindof.print_iskindof_from_universe *)
definition "OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA> = (\<lambda> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsKindOf(Person))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsKindOf(Person))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsKindOf(Person))
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsKindOf(Person)))"
definition "OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA> = (\<lambda> (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsKindOf(Planet))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsKindOf(Planet))
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsKindOf(Planet))
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsKindOf(Planet)))"
definition "OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA> = (\<lambda> (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsKindOf(Galaxy))
    | (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsKindOf(Galaxy))
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsKindOf(Galaxy))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsKindOf(Galaxy)))"
definition "OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA> = (\<lambda> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (OclAny)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (OclAny))::\<cdot>OclAny) .oclIsKindOf(OclAny))
    | (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (Person)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Person))::\<cdot>Person) .oclIsKindOf(OclAny))
    | (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (Planet)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Planet))::\<cdot>Planet) .oclIsKindOf(OclAny))
    | (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (Galaxy)) \<Rightarrow> (((((\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)) (Galaxy))::\<cdot>Galaxy) .oclIsKindOf(OclAny)))"

(* 80 ************************************ 459 + 1 *)  (* term Floor1_iskindof.print_iskindof_lemmas_id *)
lemmas[simp,code_unfold] = OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny

(* 81 ************************************ 460 + 1 *)
subsection \<open>Context Passing\<close>

(* 82 ************************************ 461 + 64 *)  (* term Floor1_iskindof.print_iskindof_lemma_cp *)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsKindOf(Person)))))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp only: cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person)
lemma cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsKindOf(Planet)))))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet)
lemma cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsKindOf(Galaxy)))))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet)
by(simp only: cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>OclAny) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>OclAny) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>OclAny) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>OclAny) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Person) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Person) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Person) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Person) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Planet) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Planet) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Planet) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Planet) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>OclAny)))::\<cdot>Galaxy) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Person)))::\<cdot>Galaxy) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Planet)))::\<cdot>Galaxy) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy)
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy : "(cp (p)) \<Longrightarrow> (cp ((\<lambda>x. (((p ((x::\<cdot>Galaxy)))::\<cdot>Galaxy) .oclIsKindOf(OclAny)))))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
  apply((rule cpI2[where f = "(or)"], (rule allI)+, rule cp_OclOr)+)
  apply(simp only: cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy)
by(simp only: cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy)

(* 83 ************************************ 525 + 1 *)  (* term Floor1_iskindof.print_iskindof_lemmas_cp *)
lemmas[simp,code_unfold] = cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_OclAny
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_OclAny
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_OclAny
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_OclAny
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Galaxy
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Galaxy
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Galaxy
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Galaxy
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Planet
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Planet
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Planet
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Planet
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_Person
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_Person
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_Person
                            cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_OclAny
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_OclAny
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_OclAny
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_OclAny
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Galaxy
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Galaxy
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Galaxy
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Galaxy
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Planet
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Planet
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Planet
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Planet
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_Person
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_Person
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_Person
                            cp_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Galaxy
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Planet
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_Person
                            cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_Person

(* 84 ************************************ 526 + 1 *)
subsection \<open>Execution with Invalid or Null as Argument\<close>

(* 85 ************************************ 527 + 32 *)  (* term Floor1_iskindof.print_iskindof_lemma_strict *)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid : "((invalid::\<cdot>Person) .oclIsKindOf(Person)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null : "((null::\<cdot>Person) .oclIsKindOf(Person)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsKindOf(Person)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null : "((null::\<cdot>Planet) .oclIsKindOf(Person)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsKindOf(Person)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsKindOf(Person)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsKindOf(Person)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null : "((null::\<cdot>OclAny) .oclIsKindOf(Person)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsKindOf(Planet)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null : "((null::\<cdot>Planet) .oclIsKindOf(Planet)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsKindOf(Planet)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsKindOf(Planet)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsKindOf(Planet)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null : "((null::\<cdot>OclAny) .oclIsKindOf(Planet)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid : "((invalid::\<cdot>Person) .oclIsKindOf(Planet)) = invalid"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid, simp)
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null : "((null::\<cdot>Person) .oclIsKindOf(Planet)) = true"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsKindOf(Galaxy)) = invalid"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsKindOf(Galaxy)) = true"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsKindOf(Galaxy)) = invalid"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null : "((null::\<cdot>OclAny) .oclIsKindOf(Galaxy)) = true"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid : "((invalid::\<cdot>Person) .oclIsKindOf(Galaxy)) = invalid"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null : "((null::\<cdot>Person) .oclIsKindOf(Galaxy)) = true"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsKindOf(Galaxy)) = invalid"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid, simp)
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null : "((null::\<cdot>Planet) .oclIsKindOf(Galaxy)) = true"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid : "((invalid::\<cdot>OclAny) .oclIsKindOf(OclAny)) = invalid"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null : "((null::\<cdot>OclAny) .oclIsKindOf(OclAny)) = true"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid : "((invalid::\<cdot>Person) .oclIsKindOf(OclAny)) = invalid"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null : "((null::\<cdot>Person) .oclIsKindOf(OclAny)) = true"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid : "((invalid::\<cdot>Planet) .oclIsKindOf(OclAny)) = invalid"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null : "((null::\<cdot>Planet) .oclIsKindOf(OclAny)) = true"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid : "((invalid::\<cdot>Galaxy) .oclIsKindOf(OclAny)) = invalid"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid, simp)
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null : "((null::\<cdot>Galaxy) .oclIsKindOf(OclAny)) = true"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null, simp)

(* 86 ************************************ 559 + 1 *)  (* term Floor1_iskindof.print_iskindof_lemmas_strict *)
lemmas[simp,code_unfold] = OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_invalid
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_invalid
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_invalid
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_invalid
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_null
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_null
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_null
                            OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_null
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_invalid
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_invalid
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_invalid
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_invalid
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_null
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_null
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_null
                            OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_null
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_invalid
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_invalid
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_invalid
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_invalid
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_null
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_null
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_null
                            OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_null
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_invalid
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_invalid
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_invalid
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_invalid
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_null
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_null
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_null
                            OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_null

(* 87 ************************************ 560 + 1 *)
subsection \<open>Validity and Definedness Properties\<close>

(* 88 ************************************ 561 + 16 *)  (* term Floor1_iskindof.print_iskindof_defined *)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(Person)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person, rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined[OF isdef])
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(Person)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet, rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined[OF isdef])
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(Person)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy, rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined[OF isdef])
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(Person)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, rule OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined[OF isdef])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(Planet)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet, rule defined_or_I[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined[OF isdef]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(Planet)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy, rule defined_or_I[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined[OF isdef]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(Planet)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny, rule defined_or_I[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined[OF isdef]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(Planet)))"
by(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, rule defined_or_I[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined[OF isdef]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(Galaxy)))"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy, rule defined_or_I[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined[OF isdef]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy)))"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny, rule defined_or_I[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined[OF isdef]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(Galaxy)))"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, rule defined_or_I[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined[OF isdef]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(Galaxy)))"
by(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet, rule defined_or_I[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined[OF isdef]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(OclAny)))"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny, rule defined_or_I[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined[OF isdef]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(OclAny)))"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, rule defined_or_I[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined[OF isdef]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(OclAny)))"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet, rule defined_or_I[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined[OF isdef]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined :
assumes isdef: "\<tau> \<Turnstile> (\<upsilon> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(OclAny)))"
by(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy, rule defined_or_I[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined[OF isdef]])

(* 89 ************************************ 577 + 16 *)  (* term Floor1_iskindof.print_iskindof_defined' *)
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(Person)))"
by(rule OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(Person)))"
by(rule OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(Person)))"
by(rule OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(Person)))"
by(rule OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(Planet)))"
by(rule OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(Planet)))"
by(rule OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(Planet)))"
by(rule OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(Planet)))"
by(rule OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(Galaxy)))"
by(rule OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy)))"
by(rule OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(Galaxy)))"
by(rule OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(Galaxy)))"
by(rule OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>OclAny) .oclIsKindOf(OclAny)))"
by(rule OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .oclIsKindOf(OclAny)))"
by(rule OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .oclIsKindOf(OclAny)))"
by(rule OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet_defined[OF isdef[THEN foundation20]])
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined' :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .oclIsKindOf(OclAny)))"
by(rule OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy_defined[OF isdef[THEN foundation20]])

(* 90 ************************************ 593 + 1 *)
subsection \<open>Up Down Casting\<close>

(* 91 ************************************ 594 + 4 *)  (* term Floor1_iskindof.print_iskindof_up_eq_asty *)
lemma actual_eq_static\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsKindOf(Person))"
  apply(simp only: OclValid_def, insert isdef)
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person)
  apply(auto simp: foundation16 bot_option_def split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
by((simp_all add: false_def true_def OclOr_def OclAnd_def OclNot_def)?)
lemma actual_eq_static\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsKindOf(Planet))"
  apply(simp only: OclValid_def, insert isdef)
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet, subst (1) cp_OclOr, simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
  apply(auto simp: cp_OclOr[symmetric ] foundation16 bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet split: option.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
by((simp_all add: false_def true_def OclOr_def OclAnd_def OclNot_def)?)
lemma actual_eq_static\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Galaxy))"
  apply(simp only: OclValid_def, insert isdef)
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy, subst (1) cp_OclOr, simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy, subst (2 1) cp_OclOr, simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
  apply(auto simp: cp_OclOr[symmetric ] foundation16 bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy split: option.split ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split)
by((simp_all add: false_def true_def OclOr_def OclAnd_def OclNot_def)?)
lemma actual_eq_static\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(OclAny))"
  apply(simp only: OclValid_def, insert isdef)
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny, subst (1) cp_OclOr, simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny, subst (2 1) cp_OclOr, simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny, subst (3 2 1) cp_OclOr, simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
  apply(auto simp: cp_OclOr[symmetric ] foundation16 bot_option_def OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny split: option.split ty\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split ty\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split ty\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t.split ty\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split ty\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y.split)
by((simp_all add: false_def true_def OclOr_def OclAnd_def OclNot_def)?)

(* 92 ************************************ 598 + 6 *)  (* term Floor1_iskindof.print_iskindof_up_larger *)
lemma actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsKindOf(Planet))"
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
by(rule foundation25', rule actual_eq_static\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n[OF isdef])
lemma actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsKindOf(Galaxy))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
by(rule foundation25', rule actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t[OF isdef])
lemma actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Person) .oclIsKindOf(OclAny))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
by(rule foundation25', rule actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[OF isdef])
lemma actualKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsKindOf(Galaxy))"
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
by(rule foundation25', rule actual_eq_static\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t[OF isdef])
lemma actualKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticKind\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsKindOf(OclAny))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
by(rule foundation25', rule actualKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[OF isdef])
lemma actualKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_larger_staticKind\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(OclAny))"
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
by(rule foundation25', rule actual_eq_static\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[OF isdef])

(* 93 ************************************ 604 + 6 *)  (* term Floor1_iskindof.print_iskindof_up_istypeof_unfold *)
lemma not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Planet_OclIsTypeOf_others_unfold :
assumes isdef: "(\<tau> \<Turnstile> (\<delta> (X)))"
assumes iskin: "(\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsKindOf(Person)))"
shows "(\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsTypeOf(Person)))"
  using iskin
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Galaxy_OclIsTypeOf_others_unfold :
assumes isdef: "(\<tau> \<Turnstile> (\<delta> (X)))"
assumes iskin: "(\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Person)))"
shows "(\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Person)))"
  using iskin
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_OclAny_OclIsTypeOf_others_unfold :
assumes isdef: "(\<tau> \<Turnstile> (\<delta> (X)))"
assumes iskin: "(\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Person)))"
shows "(\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Person)))"
  using iskin
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_Galaxy_OclIsTypeOf_others_unfold :
assumes isdef: "(\<tau> \<Turnstile> (\<delta> (X)))"
assumes iskin: "(\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Planet)))"
shows "((\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Planet))) \<or> (\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Person))))"
  using iskin
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined'[OF isdef]])
  apply(simp)
  apply(drule not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Galaxy_OclIsTypeOf_others_unfold[OF isdef], blast)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_OclAny_OclIsTypeOf_others_unfold :
assumes isdef: "(\<tau> \<Turnstile> (\<delta> (X)))"
assumes iskin: "(\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Planet)))"
shows "((\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Planet))) \<or> (\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Person))))"
  using iskin
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(drule not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_OclAny_OclIsTypeOf_others_unfold[OF isdef], blast)
done
lemma not_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_then_OclAny_OclIsTypeOf_others_unfold :
assumes isdef: "(\<tau> \<Turnstile> (\<delta> (X)))"
assumes iskin: "(\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy)))"
shows "((\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy))) \<or> ((\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Person))) \<or> (\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Planet)))))"
  using iskin
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(drule not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_OclAny_OclIsTypeOf_others_unfold[OF isdef], blast)
done

(* 94 ************************************ 610 + 6 *)  (* term Floor1_iskindof.print_iskindof_up_istypeof *)
lemma not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Planet_OclIsTypeOf_others :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsKindOf(Person))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsTypeOf(Planet))"
  using actual_eq_static\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t[OF isdef]
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet_defined'[OF isdef]])
  apply(simp)
  apply(simp add: iskin)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Galaxy_OclIsTypeOf_others :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Person))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "(\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Galaxy)) \<or> \<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Planet)))"
  using actual_eq_static\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[OF isdef]
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined'[OF isdef]])
  apply(simp)
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy_defined'[OF isdef]])
  apply(simp)
  apply(simp add: iskin)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_OclAny_OclIsTypeOf_others :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Person))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "(\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny)) \<or> (\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy)) \<or> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Planet))))"
  using actual_eq_static\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[OF isdef]
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(simp only: OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(simp add: iskin)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_Galaxy_OclIsTypeOf_others :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsTypeOf(Galaxy))"
  using actual_eq_static\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[OF isdef]
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy_defined'[OF isdef]])
  apply(simp)
  apply(simp add: iskin)
done
lemma not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_OclAny_OclIsTypeOf_others :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "(\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny)) \<or> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(Galaxy)))"
  using actual_eq_static\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[OF isdef]
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(simp only: OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(simp add: iskin)
done
lemma not_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_then_OclAny_OclIsTypeOf_others :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsTypeOf(OclAny))"
  using actual_eq_static\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[OF isdef]
  apply(simp only: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply(erule foundation26[OF OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_defined'[OF isdef], OF OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny_defined'[OF isdef]])
  apply(simp)
  apply(simp add: iskin)
done

(* 95 ************************************ 616 + 10 *)  (* term Floor1_iskindof.print_iskindof_up_d_cast *)
lemma down_cast_kind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_from_Planet_to_Person :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Planet) .oclIsKindOf(Person))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Planet_OclIsTypeOf_others[OF iskin, OF isdef])
  apply(rule down_cast_type\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_Planet_to_Person, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_from_Galaxy_to_Person :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Person))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_Galaxy_OclIsTypeOf_others[OF iskin, OF isdef], elim disjE)
  apply(rule down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_Galaxy_to_Person, simp only: , simp only: isdef)
  apply(rule down_cast_type\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_Galaxy_to_Person, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_from_OclAny_to_Person :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Person))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_then_OclAny_OclIsTypeOf_others[OF iskin, OF isdef], elim disjE)
  apply(rule down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Person, simp only: , simp only: isdef)
  apply(rule down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Person, simp only: , simp only: isdef)
  apply(rule down_cast_type\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_OclAny_to_Person, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_Galaxy_to_Planet :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Planet)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_Galaxy_OclIsTypeOf_others[OF iskin, OF isdef])
  apply(rule down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_Galaxy_to_Planet, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_Galaxy_to_Person :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>Galaxy) .oclIsKindOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_Galaxy_OclIsTypeOf_others[OF iskin, OF isdef])
  apply(rule down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_Galaxy_to_Person, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_OclAny_to_Planet :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Planet)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_OclAny_OclIsTypeOf_others[OF iskin, OF isdef], elim disjE)
  apply(rule down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Planet, simp only: , simp only: isdef)
  apply(rule down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Planet, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_from_OclAny_to_Person :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Planet))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_then_OclAny_OclIsTypeOf_others[OF iskin, OF isdef], elim disjE)
  apply(rule down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Person, simp only: , simp only: isdef)
  apply(rule down_cast_type\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Person, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Galaxy :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Galaxy)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_then_OclAny_OclIsTypeOf_others[OF iskin, OF isdef])
  apply(rule down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Galaxy, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Person :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Person)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_then_OclAny_OclIsTypeOf_others[OF iskin, OF isdef])
  apply(rule down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Person, simp only: , simp only: isdef)
done
lemma down_cast_kind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_from_OclAny_to_Planet :
assumes iskin: "\<not> \<tau> \<Turnstile> ((X::\<cdot>OclAny) .oclIsKindOf(Galaxy))"
assumes isdef: "\<tau> \<Turnstile> (\<delta> (X))"
shows "\<tau> \<Turnstile> (X .oclAsType(Planet)) \<triangleq> invalid"
  apply(insert not_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_then_OclAny_OclIsTypeOf_others[OF iskin, OF isdef])
  apply(rule down_cast_type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_from_OclAny_to_Planet, simp only: , simp only: isdef)
done

(* 96 ************************************ 626 + 1 *)
subsection \<open>Const\<close>

(* 97 ************************************ 627 + 1 *)
section \<open>Class Model: OclAllInstances\<close>

(* 98 ************************************ 628 + 1 *)
text \<open>
   To denote \OCL-types occurring in \OCL expressions syntactically---as, for example,  as
``argument'' of \inlineisar{oclAllInstances()}---we use the inverses of the injection
functions into the object universes; we show that this is sufficient ``characterization.'' \<close>

(* 99 ************************************ 629 + 4 *)  (* term Floor1_allinst.print_allinst_def_id *)
definition "Person = OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>"
definition "Planet = OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA>"
definition "Galaxy = OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA>"
definition "OclAny = OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>"

(* 100 ************************************ 633 + 1 *)  (* term Floor1_allinst.print_allinst_lemmas_id *)
lemmas[simp,code_unfold] = Person_def
                            Planet_def
                            Galaxy_def
                            OclAny_def

(* 101 ************************************ 634 + 1 *)  (* term Floor1_allinst.print_allinst_astype *)
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>_some : "(OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA> (x)) \<noteq> None"
by(simp add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>_def)

(* 102 ************************************ 635 + 3 *)  (* term Floor1_allinst.print_allinst_exec *)
lemma OclAllInstances_generic\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec :
shows "(OclAllInstances_generic (pre_post) (OclAny)) = (\<lambda>\<tau>. (Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e (\<lfloor>\<lfloor>Some ` OclAny ` (ran ((heap ((pre_post (\<tau>))))))\<rfloor>\<rfloor>)))"
  proof - let ?S1 = "(\<lambda>\<tau>. OclAny ` (ran ((heap ((pre_post (\<tau>)))))))" show ?thesis
  proof - let ?S2 = "(\<lambda>\<tau>. ((?S1) (\<tau>)) - {None})" show ?thesis
  proof - have B: "(\<And>\<tau>. ((?S2) (\<tau>)) \<subseteq> ((?S1) (\<tau>)))" by(auto) show ?thesis
  proof - have C: "(\<And>\<tau>. ((?S1) (\<tau>)) \<subseteq> ((?S2) (\<tau>)))" by(auto simp: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>_some) show ?thesis
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
by(insert equalityI[OF B, OF C], simp) qed qed qed qed
lemma OclAllInstances_at_post\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec :
shows "(OclAllInstances_at_post (OclAny)) = (\<lambda>\<tau>. (Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e (\<lfloor>\<lfloor>Some ` OclAny ` (ran ((heap ((snd (\<tau>))))))\<rfloor>\<rfloor>)))"
  unfolding OclAllInstances_at_post_def
by(rule OclAllInstances_generic\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec)
lemma OclAllInstances_at_pre\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec :
shows "(OclAllInstances_at_pre (OclAny)) = (\<lambda>\<tau>. (Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e (\<lfloor>\<lfloor>Some ` OclAny ` (ran ((heap ((fst (\<tau>))))))\<rfloor>\<rfloor>)))"
  unfolding OclAllInstances_at_pre_def
by(rule OclAllInstances_generic\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec)

(* 103 ************************************ 638 + 1 *)
subsection \<open>OclIsTypeOf\<close>

(* 104 ************************************ 639 + 2 *)  (* term Floor1_allinst.print_allinst_istypeof_pre *)
lemma ex_ssubst : "(\<forall>x \<in> B. (s (x)) = (t (x))) \<Longrightarrow> (\<exists>x \<in> B. (P ((s (x))))) = (\<exists>x \<in> B. (P ((t (x)))))"
by(simp)
lemma ex_def : "x \<in> \<lceil>\<lceil>\<lfloor>\<lfloor>Some ` (X - {None})\<rfloor>\<rfloor>\<rceil>\<rceil> \<Longrightarrow> (\<exists>y. x = \<lfloor>\<lfloor>y\<rfloor>\<rfloor>)"
by(auto)

(* 105 ************************************ 641 + 21 *)  (* term Floor1_allinst.print_allinst_istypeof *)
lemma Person_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Person))) (OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsTypeOf(Person)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actual_eq_static\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n[simplified OclValid_def, simplified OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Person_OclAllInstances_at_post_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Person))) (OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))"
  unfolding OclAllInstances_at_post_def
by(rule Person_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
lemma Person_OclAllInstances_at_pre_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Person))) (OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))"
  unfolding OclAllInstances_at_pre_def
by(rule Person_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
lemma Planet_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t1 :
assumes [simp]: "(\<And>x. (pre_post ((x , x))) = x)"
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Planet))) (OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)))"
  apply(rule exI[where x = "\<tau>\<^sub>0"], simp add: \<tau>\<^sub>0_def OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
by(simp)
lemma Planet_OclAllInstances_at_post_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t1 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Planet))) (OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)))"
  unfolding OclAllInstances_at_post_def
by(rule Planet_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t1, simp)
lemma Planet_OclAllInstances_at_pre_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t1 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Planet))) (OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)))"
  unfolding OclAllInstances_at_pre_def
by(rule Planet_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t1, simp)
lemma Planet_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t2 :
assumes [simp]: "(\<And>x. (pre_post ((x , x))) = x)"
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Planet))) (OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)))))"
  proof - fix oid a show ?thesis
  proof - let ?t0 = "(state.make ((Map.empty (oid \<mapsto> (in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (a))) (None) (None))))))) (Map.empty))" show ?thesis
  apply(rule exI[where x = "(?t0 , ?t0)"], simp add: OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA>_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
by(simp add: state.make_def OclNot_def) qed qed
lemma Planet_OclAllInstances_at_post_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t2 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_at_post (Planet))) (OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)))))"
  unfolding OclAllInstances_at_post_def
by(rule Planet_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t2, simp)
lemma Planet_OclAllInstances_at_pre_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t2 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_at_pre (Planet))) (OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)))))"
  unfolding OclAllInstances_at_pre_def
by(rule Planet_OclAllInstances_generic_OclIsTypeOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t2, simp)
lemma Galaxy_OclAllInstances_generic_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y1 :
assumes [simp]: "(\<And>x. (pre_post ((x , x))) = x)"
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Galaxy))) (OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)))"
  apply(rule exI[where x = "\<tau>\<^sub>0"], simp add: \<tau>\<^sub>0_def OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
by(simp)
lemma Galaxy_OclAllInstances_at_post_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y1 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Galaxy))) (OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)))"
  unfolding OclAllInstances_at_post_def
by(rule Galaxy_OclAllInstances_generic_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y1, simp)
lemma Galaxy_OclAllInstances_at_pre_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y1 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Galaxy))) (OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)))"
  unfolding OclAllInstances_at_pre_def
by(rule Galaxy_OclAllInstances_generic_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y1, simp)
lemma Galaxy_OclAllInstances_generic_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y2 :
assumes [simp]: "(\<And>x. (pre_post ((x , x))) = x)"
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Galaxy))) (OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)))))"
  proof - fix oid a show ?thesis
  proof - let ?t0 = "(state.make ((Map.empty (oid \<mapsto> (in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y ((mk\<E>\<X>\<T>\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (a))) (None) (None) (None))))))) (Map.empty))" show ?thesis
  apply(rule exI[where x = "(?t0 , ?t0)"], simp add: OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA>_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
by(simp add: state.make_def OclNot_def) qed qed
lemma Galaxy_OclAllInstances_at_post_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y2 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_at_post (Galaxy))) (OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)))))"
  unfolding OclAllInstances_at_post_def
by(rule Galaxy_OclAllInstances_generic_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y2, simp)
lemma Galaxy_OclAllInstances_at_pre_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y2 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_at_pre (Galaxy))) (OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)))))"
  unfolding OclAllInstances_at_pre_def
by(rule Galaxy_OclAllInstances_generic_OclIsTypeOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y2, simp)
lemma OclAny_OclAllInstances_generic_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1 :
assumes [simp]: "(\<And>x. (pre_post ((x , x))) = x)"
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (OclAny))) (OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))"
  apply(rule exI[where x = "\<tau>\<^sub>0"], simp add: \<tau>\<^sub>0_def OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
by(simp)
lemma OclAny_OclAllInstances_at_post_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (OclAny))) (OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))"
  unfolding OclAllInstances_at_post_def
by(rule OclAny_OclAllInstances_generic_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1, simp)
lemma OclAny_OclAllInstances_at_pre_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (OclAny))) (OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))"
  unfolding OclAllInstances_at_pre_def
by(rule OclAny_OclAllInstances_generic_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1, simp)
lemma OclAny_OclAllInstances_generic_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2 :
assumes [simp]: "(\<And>x. (pre_post ((x , x))) = x)"
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_generic (pre_post) (OclAny))) (OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))))"
  proof - fix oid a show ?thesis
  proof - let ?t0 = "(state.make ((Map.empty (oid \<mapsto> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (a))))))))) (Map.empty))" show ?thesis
  apply(rule exI[where x = "(?t0 , ?t0)"], simp add: OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
by(simp add: state.make_def OclNot_def) qed qed
lemma OclAny_OclAllInstances_at_post_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_at_post (OclAny))) (OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))))"
  unfolding OclAllInstances_at_post_def
by(rule OclAny_OclAllInstances_generic_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2, simp)
lemma OclAny_OclAllInstances_at_pre_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2 :
shows "(\<exists>\<tau>. \<tau> \<Turnstile> (not ((UML_Set.OclForall ((OclAllInstances_at_pre (OclAny))) (OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))))"
  unfolding OclAllInstances_at_pre_def
by(rule OclAny_OclAllInstances_generic_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2, simp)

(* 106 ************************************ 662 + 1 *)
subsection \<open>OclIsKindOf\<close>

(* 107 ************************************ 663 + 12 *)  (* term Floor1_allinst.print_allinst_iskindof_eq *)
lemma Person_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Person))) (OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(Person)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actual_eq_static\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Person_OclAllInstances_at_post_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Person))) (OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))"
  unfolding OclAllInstances_at_post_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
lemma Person_OclAllInstances_at_pre_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Person))) (OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))"
  unfolding OclAllInstances_at_pre_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
lemma Planet_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Planet))) (OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Planet)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(Planet)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actual_eq_static\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Planet_OclAllInstances_at_post_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Planet))) (OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t))"
  unfolding OclAllInstances_at_post_def
by(rule Planet_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)
lemma Planet_OclAllInstances_at_pre_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Planet))) (OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t))"
  unfolding OclAllInstances_at_pre_def
by(rule Planet_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)
lemma Galaxy_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Galaxy))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Galaxy)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(Galaxy)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actual_eq_static\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Galaxy_OclAllInstances_at_post_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Galaxy))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule Galaxy_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)
lemma Galaxy_OclAllInstances_at_pre_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Galaxy))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule Galaxy_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)
lemma OclAny_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (OclAny))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(OclAny)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actual_eq_static\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma OclAny_OclAllInstances_at_post_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (OclAny))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule OclAny_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)
lemma OclAny_OclAllInstances_at_pre_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (OclAny))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule OclAny_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)

(* 108 ************************************ 675 + 18 *)  (* term Floor1_allinst.print_allinst_iskindof_larger *)
lemma Person_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Person))) (OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(Planet)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Person_OclAllInstances_at_post_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Person))) (OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t))"
  unfolding OclAllInstances_at_post_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)
lemma Person_OclAllInstances_at_pre_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Person))) (OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t))"
  unfolding OclAllInstances_at_pre_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t)
lemma Person_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Person))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(Galaxy)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Person_OclAllInstances_at_post_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Person))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)
lemma Person_OclAllInstances_at_pre_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Person))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)
lemma Person_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Person))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(OclAny)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actualKind\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_larger_staticKind\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Person_OclAllInstances_at_post_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Person))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)
lemma Person_OclAllInstances_at_pre_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Person))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule Person_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)
lemma Planet_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Planet))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(Galaxy)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actualKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Planet_OclAllInstances_at_post_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Planet))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule Planet_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)
lemma Planet_OclAllInstances_at_pre_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Planet))) (OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule Planet_OclAllInstances_generic_OclIsKindOf\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y)
lemma Planet_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Planet))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(OclAny)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actualKind\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_larger_staticKind\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Planet_OclAllInstances_at_post_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Planet))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule Planet_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)
lemma Planet_OclAllInstances_at_pre_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Planet))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule Planet_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)
lemma Galaxy_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y : "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_generic (pre_post) (Galaxy))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  apply(simp add: OclValid_def del: OclAllInstances_generic_def OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy)
  apply(simp only: UML_Set.OclForall_def refl if_True OclAllInstances_generic_defined[simplified OclValid_def])
  apply(simp only: OclAllInstances_generic_def)
  apply(subst (1 2 3) Abs_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inverse, simp add: bot_option_def)
  apply(subst (1 2 3) ex_ssubst[where s = "(\<lambda>x. (((\<lambda>_. x) .oclIsKindOf(OclAny)) (\<tau>)))" and t = "(\<lambda>_. (true (\<tau>)))"])
  apply(intro ballI actualKind\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_larger_staticKind\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y[simplified OclValid_def])
  apply(drule ex_def, erule exE, simp)
by(simp)
lemma Galaxy_OclAllInstances_at_post_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Galaxy))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_post_def
by(rule Galaxy_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)
lemma Galaxy_OclAllInstances_at_pre_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :
shows "\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Galaxy))) (OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))"
  unfolding OclAllInstances_at_pre_def
by(rule Galaxy_OclAllInstances_generic_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)

(* 109 ************************************ 693 + 1 *)
section \<open>Class Model: The Accessors\<close>

(* 110 ************************************ 694 + 1 *)
text \<open>
  \label{sec:Employee-DesignModel-UMLPart-generated-generatededm-accessors}\<close>

(* 111 ************************************ 695 + 1 *)
text \<open>\<close>

(* 112 ************************************ 696 + 1 *)
subsection \<open>Definition\<close>

(* 113 ************************************ 697 + 1 *)
text \<open>\<close>

(* 114 ************************************ 698 + 1 *)  (* term Floor1_access.print_access_oid_uniq_ml *)
ML \<open>val oidPerson_0_boss = 0\<close>

(* 115 ************************************ 699 + 1 *)  (* term Floor1_access.print_access_oid_uniq *)
definition "oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss = 0"

(* 116 ************************************ 700 + 1 *)
text \<open>\<close>

(* 117 ************************************ 701 + 5 *)  (* term Floor1_access.print_access_eval_extract *)
definition "eval_extract x f = (\<lambda>\<tau>. (case x \<tau> of \<lfloor>\<lfloor>obj\<rfloor>\<rfloor> \<Rightarrow> (f ((oid_of (obj))) (\<tau>))
    | _ \<Rightarrow> invalid \<tau>))"
definition "in_pre_state = fst"
definition "in_post_state = snd"
definition "reconst_basetype = (\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>)"
definition "reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d x = Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e o (reconst_basetype (x))"

(* 118 ************************************ 706 + 1 *)
text \<open>\<close>

(* 119 ************************************ 707 + 2 *)  (* term Floor1_access.print_access_choose_ml *)
ML \<open>val switch2_01 = (fn [x0 , x1] => (x0 , x1))\<close>
ML \<open>val switch2_10 = (fn [x0 , x1] => (x1 , x0))\<close>

(* 120 ************************************ 709 + 3 *)  (* term Floor1_access.print_access_choose *)
definition "switch\<^sub>2_01 = (\<lambda> [x0 , x1] \<Rightarrow> (x0 , x1))"
definition "switch\<^sub>2_10 = (\<lambda> [x0 , x1] \<Rightarrow> (x1 , x0))"
definition "deref_assocs pre_post to_from assoc_oid f oid = (\<lambda>\<tau>. (case (assocs ((pre_post (\<tau>))) (assoc_oid)) of \<lfloor>S\<rfloor> \<Rightarrow> (f ((deref_assocs_list (to_from) (oid) (S))) (\<tau>))
    | _ \<Rightarrow> (invalid (\<tau>))))"

(* 121 ************************************ 712 + 4 *)  (* term Floor1_access.print_access_deref_oid *)
definition "deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n fst_snd f oid = (\<lambda>\<tau>. (case (heap (fst_snd \<tau>) (oid)) of \<lfloor>in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n obj\<rfloor> \<Rightarrow> f obj \<tau>
    | _ \<Rightarrow> invalid \<tau>))"
definition "deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t fst_snd f oid = (\<lambda>\<tau>. (case (heap (fst_snd \<tau>) (oid)) of \<lfloor>in\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t obj\<rfloor> \<Rightarrow> f obj \<tau>
    | _ \<Rightarrow> invalid \<tau>))"
definition "deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y fst_snd f oid = (\<lambda>\<tau>. (case (heap (fst_snd \<tau>) (oid)) of \<lfloor>in\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y obj\<rfloor> \<Rightarrow> f obj \<tau>
    | _ \<Rightarrow> invalid \<tau>))"
definition "deref_oid\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y fst_snd f oid = (\<lambda>\<tau>. (case (heap (fst_snd \<tau>) (oid)) of \<lfloor>in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y obj\<rfloor> \<Rightarrow> f obj \<tau>
    | _ \<Rightarrow> invalid \<tau>))"

(* 122 ************************************ 716 + 0 *)  (* term Floor1_access.print_access_deref_assocs *)

(* 123 ************************************ 716 + 1 *)
text \<open>
   pointer undefined in state or not referencing a type conform object representation \<close>

(* 124 ************************************ 717 + 15 *)  (* term Floor1_access.print_access_select *)
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (\<bottom>) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (\<lfloor>x___boss\<rfloor>) (_)) \<Rightarrow> (f (x___boss)))"
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (\<bottom>)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (\<lfloor>x___salary\<rfloor>)) \<Rightarrow> (f (x___salary)))"
definition "select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole f = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (\<bottom>) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (\<lfloor>x___wormhole\<rfloor>) (_)) \<Rightarrow> (f (x___wormhole)))"
definition "select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight f = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (\<bottom>)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (\<lfloor>x___weight\<rfloor>)) \<Rightarrow> (f (x___weight)))"
definition "select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound f = (\<lambda> (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_) (\<bottom>) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_) (\<lfloor>x___sound\<rfloor>) (_) (_)) \<Rightarrow> (f (x___sound)))"
definition "select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving f = (\<lambda> (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_) (_) (\<bottom>) (_)) \<Rightarrow> null
    | (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_) (_) (\<lfloor>x___moving\<rfloor>) (_)) \<Rightarrow> (f (x___moving)))"
definition "select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world f = (\<lambda> (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_) (_) (_) (\<bottom>)) \<Rightarrow> null
    | (mk\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (_) (_) (_) (\<lfloor>x___outer_world\<rfloor>)) \<Rightarrow> (f (x___outer_world)))"
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (\<bottom>) (_) (_) (_) (_))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (\<lfloor>x___wormhole\<rfloor>) (_) (_) (_) (_))) (_) (_)) \<Rightarrow> (f (x___wormhole)))"
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (\<bottom>) (_) (_) (_))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (\<lfloor>x___weight\<rfloor>) (_) (_) (_))) (_) (_)) \<Rightarrow> (f (x___weight)))"
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (\<bottom>) (_) (_))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (\<lfloor>x___sound\<rfloor>) (_) (_))) (_) (_)) \<Rightarrow> (f (x___sound)))"
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (_) (\<bottom>) (_))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (_) (\<lfloor>x___moving\<rfloor>) (_))) (_) (_)) \<Rightarrow> (f (x___moving)))"
definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world f = (\<lambda> (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (_) (_) (\<bottom>))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (_) (_) (_) (_) (_) (\<lfloor>x___outer_world\<rfloor>))) (_) (_)) \<Rightarrow> (f (x___outer_world)))"
definition "select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound f = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (\<bottom>) (_) (_))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (\<lfloor>x___sound\<rfloor>) (_) (_))) (_) (_)) \<Rightarrow> (f (x___sound))
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (person))) (_) (_)) \<Rightarrow> (select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound (f) (person)))"
definition "select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving f = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (\<bottom>) (_))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (\<lfloor>x___moving\<rfloor>) (_))) (_) (_)) \<Rightarrow> (f (x___moving))
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (person))) (_) (_)) \<Rightarrow> (select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving (f) (person)))"
definition "select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world f = (\<lambda> (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (_) (\<bottom>))) (_) (_)) \<Rightarrow> null
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (_) (_) (_) (\<lfloor>x___outer_world\<rfloor>))) (_) (_)) \<Rightarrow> (f (x___outer_world))
    | (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (person))) (_) (_)) \<Rightarrow> (select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world (f) (person)))"

(* 125 ************************************ 732 + 0 *)  (* term Floor1_access.print_access_select_obj *)

(* 126 ************************************ 732 + 14 *)  (* term Floor1_access.print_access_dot_consts *)
consts dot_0___boss :: "(\<AA>, '\<alpha>) val \<Rightarrow> \<cdot>Person" ("(_) .boss")
consts dot_0___bossat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> \<cdot>Person" ("(_) .boss@pre")
consts dot__salary :: "(\<AA>, '\<alpha>) val \<Rightarrow> Integer" ("(_) .salary")
consts dot__salaryat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> Integer" ("(_) .salary@pre")
consts dot__wormhole :: "(\<AA>, '\<alpha>) val \<Rightarrow> (\<AA>, nat option option) val" ("(_) .wormhole")
consts dot__wormholeat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> (\<AA>, nat option option) val" ("(_) .wormhole@pre")
consts dot__weight :: "(\<AA>, '\<alpha>) val \<Rightarrow> Integer" ("(_) .weight")
consts dot__weightat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> Integer" ("(_) .weight@pre")
consts dot__sound :: "(\<AA>, '\<alpha>) val \<Rightarrow> Void" ("(_) .sound")
consts dot__soundat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> Void" ("(_) .sound@pre")
consts dot__moving :: "(\<AA>, '\<alpha>) val \<Rightarrow> Boolean" ("(_) .moving")
consts dot__movingat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> Boolean" ("(_) .moving@pre")
consts dot__outer_world :: "(\<AA>, '\<alpha>) val \<Rightarrow> Set_Sequence_Planet" ("(_) .outer'_world")
consts dot__outer_worldat_pre :: "(\<AA>, '\<alpha>) val \<Rightarrow> Set_Sequence_Planet" ("(_) .outer'_world@pre")

(* 127 ************************************ 746 + 30 *)  (* term Floor1_access.print_access_dot *)
overloading dot_0___boss \<equiv> "(dot_0___boss::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss : "(x::\<cdot>Person) .boss \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss ((select_object_any\<^sub>S\<^sub>e\<^sub>t ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) (reconst_basetype))))))))))"
end
overloading dot__salary \<equiv> "(dot__salary::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary : "(x::\<cdot>Person) .salary \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary (reconst_basetype))))))"
end
overloading dot_0___bossat_pre \<equiv> "(dot_0___bossat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre : "(x::\<cdot>Person) .boss@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss ((select_object_any\<^sub>S\<^sub>e\<^sub>t ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) (reconst_basetype))))))))))"
end
overloading dot__salaryat_pre \<equiv> "(dot__salaryat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre : "(x::\<cdot>Person) .salary@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary (reconst_basetype))))))"
end
overloading dot__wormhole \<equiv> "(dot__wormhole::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole : "(x::\<cdot>Planet) .wormhole \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole (reconst_basetype))))))"
end
overloading dot__weight \<equiv> "(dot__weight::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight : "(x::\<cdot>Planet) .weight \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight (reconst_basetype))))))"
end
overloading dot__wormholeat_pre \<equiv> "(dot__wormholeat_pre::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre : "(x::\<cdot>Planet) .wormhole@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole (reconst_basetype))))))"
end
overloading dot__weightat_pre \<equiv> "(dot__weightat_pre::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre : "(x::\<cdot>Planet) .weight@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight (reconst_basetype))))))"
end
overloading dot__sound \<equiv> "(dot__sound::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound : "(x::\<cdot>Galaxy) .sound \<equiv> (eval_extract (x) ((deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (in_post_state) ((select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound (reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d))))))"
end
overloading dot__moving \<equiv> "(dot__moving::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving : "(x::\<cdot>Galaxy) .moving \<equiv> (eval_extract (x) ((deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (in_post_state) ((select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving (reconst_basetype))))))"
end
overloading dot__outer_world \<equiv> "(dot__outer_world::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world : "(x::\<cdot>Galaxy) .outer_world \<equiv> (eval_extract (x) ((deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (in_post_state) ((select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world ((select_object\<^sub>S\<^sub>e\<^sub>t ((select_object\<^sub>S\<^sub>e\<^sub>q ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) (reconst_basetype))))))))))))"
end
overloading dot__soundat_pre \<equiv> "(dot__soundat_pre::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre : "(x::\<cdot>Galaxy) .sound@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (in_pre_state) ((select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound (reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d))))))"
end
overloading dot__movingat_pre \<equiv> "(dot__movingat_pre::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre : "(x::\<cdot>Galaxy) .moving@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (in_pre_state) ((select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving (reconst_basetype))))))"
end
overloading dot__outer_worldat_pre \<equiv> "(dot__outer_worldat_pre::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre : "(x::\<cdot>Galaxy) .outer_world@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y (in_pre_state) ((select\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world ((select_object\<^sub>S\<^sub>e\<^sub>t ((select_object\<^sub>S\<^sub>e\<^sub>q ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) (reconst_basetype))))))))))))"
end
overloading dot__wormhole \<equiv> "(dot__wormhole::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole : "(x::\<cdot>Person) .wormhole \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole (reconst_basetype))))))"
end
overloading dot__weight \<equiv> "(dot__weight::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight : "(x::\<cdot>Person) .weight \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight (reconst_basetype))))))"
end
overloading dot__sound \<equiv> "(dot__sound::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound : "(x::\<cdot>Person) .sound \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound (reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d))))))"
end
overloading dot__moving \<equiv> "(dot__moving::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving : "(x::\<cdot>Person) .moving \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving (reconst_basetype))))))"
end
overloading dot__outer_world \<equiv> "(dot__outer_world::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world : "(x::\<cdot>Person) .outer_world \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world ((select_object\<^sub>S\<^sub>e\<^sub>t ((select_object\<^sub>S\<^sub>e\<^sub>q ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) (reconst_basetype))))))))))))"
end
overloading dot__wormholeat_pre \<equiv> "(dot__wormholeat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre : "(x::\<cdot>Person) .wormhole@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole (reconst_basetype))))))"
end
overloading dot__weightat_pre \<equiv> "(dot__weightat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre : "(x::\<cdot>Person) .weight@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight (reconst_basetype))))))"
end
overloading dot__soundat_pre \<equiv> "(dot__soundat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre : "(x::\<cdot>Person) .sound@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound (reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d))))))"
end
overloading dot__movingat_pre \<equiv> "(dot__movingat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre : "(x::\<cdot>Person) .moving@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving (reconst_basetype))))))"
end
overloading dot__outer_worldat_pre \<equiv> "(dot__outer_worldat_pre::(\<cdot>Person) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre : "(x::\<cdot>Person) .outer_world@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) ((select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world ((select_object\<^sub>S\<^sub>e\<^sub>t ((select_object\<^sub>S\<^sub>e\<^sub>q ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) (reconst_basetype))))))))))))"
end
overloading dot__sound \<equiv> "(dot__sound::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound : "(x::\<cdot>Planet) .sound \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound (reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d))))))"
end
overloading dot__moving \<equiv> "(dot__moving::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving : "(x::\<cdot>Planet) .moving \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving (reconst_basetype))))))"
end
overloading dot__outer_world \<equiv> "(dot__outer_world::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world : "(x::\<cdot>Planet) .outer_world \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world ((select_object\<^sub>S\<^sub>e\<^sub>t ((select_object\<^sub>S\<^sub>e\<^sub>q ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_post_state) (reconst_basetype))))))))))))"
end
overloading dot__soundat_pre \<equiv> "(dot__soundat_pre::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre : "(x::\<cdot>Planet) .sound@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound (reconst_basetype\<^sub>V\<^sub>o\<^sub>i\<^sub>d))))))"
end
overloading dot__movingat_pre \<equiv> "(dot__movingat_pre::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre : "(x::\<cdot>Planet) .moving@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving (reconst_basetype))))))"
end
overloading dot__outer_worldat_pre \<equiv> "(dot__outer_worldat_pre::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre : "(x::\<cdot>Planet) .outer_world@pre \<equiv> (eval_extract (x) ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) ((select\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world ((select_object\<^sub>S\<^sub>e\<^sub>t ((select_object\<^sub>S\<^sub>e\<^sub>q ((deref_oid\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (in_pre_state) (reconst_basetype))))))))))))"
end

(* 128 ************************************ 776 + 1 *)  (* term Floor1_access.print_access_dot_lemmas_id *)
lemmas dot_accessor = dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre
                            dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound
                            dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving
                            dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world
                            dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre
                            dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre
                            dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre
                            dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre
                            dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre

(* 129 ************************************ 777 + 1 *)
subsection \<open>Context Passing\<close>

(* 130 ************************************ 778 + 1 *)  (* term Floor1_access.print_access_dot_cp_lemmas *)
lemmas[simp,code_unfold] = eval_extract_def

(* 131 ************************************ 779 + 30 *)  (* term Floor1_access.print_access_dot_lemma_cp *)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss : "(cp ((\<lambda>X. (X::\<cdot>Person) .boss)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary : "(cp ((\<lambda>X. (X::\<cdot>Person) .salary)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .boss@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .salary@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole : "(cp ((\<lambda>X. (X::\<cdot>Planet) .wormhole)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight : "(cp ((\<lambda>X. (X::\<cdot>Planet) .weight)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre : "(cp ((\<lambda>X. (X::\<cdot>Planet) .wormhole@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre : "(cp ((\<lambda>X. (X::\<cdot>Planet) .weight@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound : "(cp ((\<lambda>X. (X::\<cdot>Galaxy) .sound)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving : "(cp ((\<lambda>X. (X::\<cdot>Galaxy) .moving)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world : "(cp ((\<lambda>X. (X::\<cdot>Galaxy) .outer_world)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre : "(cp ((\<lambda>X. (X::\<cdot>Galaxy) .sound@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre : "(cp ((\<lambda>X. (X::\<cdot>Galaxy) .moving@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre : "(cp ((\<lambda>X. (X::\<cdot>Galaxy) .outer_world@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole : "(cp ((\<lambda>X. (X::\<cdot>Person) .wormhole)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight : "(cp ((\<lambda>X. (X::\<cdot>Person) .weight)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound : "(cp ((\<lambda>X. (X::\<cdot>Person) .sound)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving : "(cp ((\<lambda>X. (X::\<cdot>Person) .moving)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world : "(cp ((\<lambda>X. (X::\<cdot>Person) .outer_world)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .wormhole@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .weight@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .sound@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .moving@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre : "(cp ((\<lambda>X. (X::\<cdot>Person) .outer_world@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound : "(cp ((\<lambda>X. (X::\<cdot>Planet) .sound)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving : "(cp ((\<lambda>X. (X::\<cdot>Planet) .moving)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world : "(cp ((\<lambda>X. (X::\<cdot>Planet) .outer_world)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre : "(cp ((\<lambda>X. (X::\<cdot>Planet) .sound@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre : "(cp ((\<lambda>X. (X::\<cdot>Planet) .moving@pre)))"
by(auto simp: dot_accessor cp_def)
lemma cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre : "(cp ((\<lambda>X. (X::\<cdot>Planet) .outer_world@pre)))"
by(auto simp: dot_accessor cp_def)

(* 132 ************************************ 809 + 1 *)  (* term Floor1_access.print_access_dot_lemmas_cp *)
lemmas[simp,code_unfold] = cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre
                            cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound
                            cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving
                            cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world
                            cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre
                            cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre
                            cp_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre
                            cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre
                            cp_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre

(* 133 ************************************ 810 + 1 *)
subsection \<open>Execution with Invalid or Null as Argument\<close>

(* 134 ************************************ 811 + 60 *)  (* term Floor1_access.print_access_lemma_strict *)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss_invalid : "(invalid::\<cdot>Person) .boss = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss_null : "(null::\<cdot>Person) .boss = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary_invalid : "(invalid::\<cdot>Person) .salary = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary_null : "(null::\<cdot>Person) .salary = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre_invalid : "(invalid::\<cdot>Person) .boss@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre_null : "(null::\<cdot>Person) .boss@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre_invalid : "(invalid::\<cdot>Person) .salary@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre_null : "(null::\<cdot>Person) .salary@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole_invalid : "(invalid::\<cdot>Planet) .wormhole = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole_null : "(null::\<cdot>Planet) .wormhole = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight_invalid : "(invalid::\<cdot>Planet) .weight = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight_null : "(null::\<cdot>Planet) .weight = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre_invalid : "(invalid::\<cdot>Planet) .wormhole@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre_null : "(null::\<cdot>Planet) .wormhole@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre_invalid : "(invalid::\<cdot>Planet) .weight@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre_null : "(null::\<cdot>Planet) .weight@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound_invalid : "(invalid::\<cdot>Galaxy) .sound = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound_null : "(null::\<cdot>Galaxy) .sound = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving_invalid : "(invalid::\<cdot>Galaxy) .moving = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving_null : "(null::\<cdot>Galaxy) .moving = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world_invalid : "(invalid::\<cdot>Galaxy) .outer_world = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world_null : "(null::\<cdot>Galaxy) .outer_world = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre_invalid : "(invalid::\<cdot>Galaxy) .sound@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre_null : "(null::\<cdot>Galaxy) .sound@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre_invalid : "(invalid::\<cdot>Galaxy) .moving@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre_null : "(null::\<cdot>Galaxy) .moving@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre_invalid : "(invalid::\<cdot>Galaxy) .outer_world@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre_null : "(null::\<cdot>Galaxy) .outer_world@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole_invalid : "(invalid::\<cdot>Person) .wormhole = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole_null : "(null::\<cdot>Person) .wormhole = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight_invalid : "(invalid::\<cdot>Person) .weight = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight_null : "(null::\<cdot>Person) .weight = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound_invalid : "(invalid::\<cdot>Person) .sound = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound_null : "(null::\<cdot>Person) .sound = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving_invalid : "(invalid::\<cdot>Person) .moving = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving_null : "(null::\<cdot>Person) .moving = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world_invalid : "(invalid::\<cdot>Person) .outer_world = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world_null : "(null::\<cdot>Person) .outer_world = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre_invalid : "(invalid::\<cdot>Person) .wormhole@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre_null : "(null::\<cdot>Person) .wormhole@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre_invalid : "(invalid::\<cdot>Person) .weight@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre_null : "(null::\<cdot>Person) .weight@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre_invalid : "(invalid::\<cdot>Person) .sound@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre_null : "(null::\<cdot>Person) .sound@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre_invalid : "(invalid::\<cdot>Person) .moving@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre_null : "(null::\<cdot>Person) .moving@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre_invalid : "(invalid::\<cdot>Person) .outer_world@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre_null : "(null::\<cdot>Person) .outer_world@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound_invalid : "(invalid::\<cdot>Planet) .sound = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound_null : "(null::\<cdot>Planet) .sound = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving_invalid : "(invalid::\<cdot>Planet) .moving = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving_null : "(null::\<cdot>Planet) .moving = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world_invalid : "(invalid::\<cdot>Planet) .outer_world = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world_null : "(null::\<cdot>Planet) .outer_world = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre_invalid : "(invalid::\<cdot>Planet) .sound@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre_null : "(null::\<cdot>Planet) .sound@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre_invalid : "(invalid::\<cdot>Planet) .moving@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre_null : "(null::\<cdot>Planet) .moving@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre_invalid : "(invalid::\<cdot>Planet) .outer_world@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def invalid_def)
lemma dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre_null : "(null::\<cdot>Planet) .outer_world@pre = invalid"
by(rule ext, simp add: dot_accessor bot_option_def null_fun_def null_option_def)

(* 135 ************************************ 871 + 1 *)
subsection \<open>Representation in States\<close>

(* 136 ************************************ 872 + 30 *)  (* term Floor1_access.print_access_def_mono *)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .boss)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .boss)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .boss)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .salary)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .salary)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .salary)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salary_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .boss@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .boss@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .boss@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .salary@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .salary@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .salary@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__salaryat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .wormhole)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormhole_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .weight)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weight_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .wormhole@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__wormholeat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .weight@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__weightat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .sound)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__sound_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .moving)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__moving_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .outer_world)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_world_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .sound@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__soundat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .moving@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__movingat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Galaxy) .outer_world@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y__outer_worldat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .wormhole)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormhole_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .weight)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weight_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .sound)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__sound_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .moving)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__moving_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .outer_world)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_world_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .wormhole@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .wormhole@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__wormholeat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .weight@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .weight@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__weightat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .sound@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__soundat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .moving@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__movingat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .outer_world@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__outer_worldat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .sound)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__sound_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .moving)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__moving_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .outer_world)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_world_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .sound@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .sound@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__soundat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .moving@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .moving@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__movingat_pre_null)
by(simp add: defined_split)
lemma defined_mono_dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre : "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Planet) .outer_world@pre)) \<Longrightarrow> \<tau> \<Turnstile> (\<delta> (X))"
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> invalid)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "invalid"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre_invalid)
  apply(case_tac "\<tau> \<Turnstile> (X \<triangleq> null)", insert StrongEq_L_subst2[where P = "(\<lambda>x. (\<delta> (x .outer_world@pre)))" and \<tau> = "\<tau>" and x = "X" and y = "null"], simp add: foundation16' dot\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t__outer_worldat_pre_null)
by(simp add: defined_split)

(* 137 ************************************ 902 + 2 *)  (* term Floor1_access.print_access_is_repr *)
lemma is_repr_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss :
assumes def_dot: "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .boss))"
shows "(is_represented_in_state (in_post_state) (X .boss) (Person) (\<tau>))"
  apply(insert defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss[OF def_dot, simplified foundation16])
  apply(case_tac "(X (\<tau>))", simp add: bot_option_def)
  proof - fix a0 show "(X (\<tau>)) = (Some (a0)) \<Longrightarrow> ?thesis" when "(X (\<tau>)) \<noteq> null"
  apply(insert that, case_tac "a0", simp add: null_option_def bot_option_def, clarify)
  proof - fix a show "(X (\<tau>)) = (Some ((Some (a)))) \<Longrightarrow> ?thesis"
  apply(case_tac "(heap ((in_post_state (\<tau>))) ((oid_of (a))))", simp add: invalid_def bot_option_def)
  apply(insert def_dot, simp add: dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss is_represented_in_state_def select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss_def deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def in_post_state_def defined_def OclValid_def false_def true_def invalid_def bot_fun_def split: if_split_asm)
  proof - fix b show "(X (\<tau>)) = (Some ((Some (a)))) \<Longrightarrow> (heap ((in_post_state (\<tau>))) ((oid_of (a)))) = (Some (b)) \<Longrightarrow> ?thesis"
  apply(insert def_dot[simplified foundation16], auto simp: dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss is_represented_in_state_def deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def bot_option_def null_option_def)
  apply(case_tac "b", simp_all add: invalid_def bot_option_def)
  proof - fix r typeoid          let ?t = "(Some ((Some (r)))) \<in> (Some o OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>) ` (ran ((heap ((in_post_state (\<tau>))))))"
          let ?sel_any = "(select_object_any\<^sub>S\<^sub>e\<^sub>t ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) (reconst_basetype))))" show "(select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss (?sel_any) (typeoid) (\<tau>)) = (Some ((Some (r)))) \<Longrightarrow> ?t"
  apply(case_tac "typeoid", simp add: select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss_def)
  proof - fix opt show "(((case opt of None \<Rightarrow> null
    | (Some (x)) \<Rightarrow> ((?sel_any) (x)))) (\<tau>)) = (Some ((Some (r)))) \<Longrightarrow> ?t"
  apply(case_tac "opt", auto simp: null_fun_def null_option_def bot_option_def)
  proof - fix aa show "((?sel_any) (aa) (\<tau>)) = (Some ((Some (r)))) \<Longrightarrow> ?t" when "\<tau> \<Turnstile> (\<delta> (((?sel_any) (aa))))"
  apply(insert that, drule select_object_any_exec\<^sub>S\<^sub>e\<^sub>t[simplified foundation22], erule exE)
  proof - fix e show "?t" when "((?sel_any) (aa) (\<tau>)) = (Some ((Some (r))))" "((?sel_any) (aa) (\<tau>)) = (deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_post_state) (reconst_basetype) (e) (\<tau>))"
  apply(insert that, simp add: deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def)
  apply(case_tac "(heap ((in_post_state (\<tau>))) (e))", simp add: invalid_def bot_option_def, simp)
  proof - fix aaa show "(case aaa of (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (obj)) \<Rightarrow> (reconst_basetype (obj) (\<tau>))
    | _ \<Rightarrow> (invalid (\<tau>))) = (Some ((Some (r)))) \<Longrightarrow> (heap ((in_post_state (\<tau>))) (e)) = (Some (aaa)) \<Longrightarrow> ?t"
  apply(case_tac "aaa", auto simp: invalid_def bot_option_def image_def ran_def)
  apply(rule exI[where x = "(in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (r))"], simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>_def Let_def reconst_basetype_def split: if_split_asm)
by(rule) qed
  apply_end((blast)+)
 qed
  apply_end(simp add: foundation16 bot_option_def null_option_def)
 qed qed qed qed qed
  apply_end(simp_all)
 qed
lemma is_repr_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre :
assumes def_dot: "\<tau> \<Turnstile> (\<delta> ((X::\<cdot>Person) .boss@pre))"
shows "(is_represented_in_state (in_pre_state) (X .boss@pre) (Person) (\<tau>))"
  apply(insert defined_mono_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre[OF def_dot, simplified foundation16])
  apply(case_tac "(X (\<tau>))", simp add: bot_option_def)
  proof - fix a0 show "(X (\<tau>)) = (Some (a0)) \<Longrightarrow> ?thesis" when "(X (\<tau>)) \<noteq> null"
  apply(insert that, case_tac "a0", simp add: null_option_def bot_option_def, clarify)
  proof - fix a show "(X (\<tau>)) = (Some ((Some (a)))) \<Longrightarrow> ?thesis"
  apply(case_tac "(heap ((in_pre_state (\<tau>))) ((oid_of (a))))", simp add: invalid_def bot_option_def)
  apply(insert def_dot, simp add: dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre is_represented_in_state_def select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss_def deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def in_pre_state_def defined_def OclValid_def false_def true_def invalid_def bot_fun_def split: if_split_asm)
  proof - fix b show "(X (\<tau>)) = (Some ((Some (a)))) \<Longrightarrow> (heap ((in_pre_state (\<tau>))) ((oid_of (a)))) = (Some (b)) \<Longrightarrow> ?thesis"
  apply(insert def_dot[simplified foundation16], auto simp: dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___bossat_pre is_represented_in_state_def deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def bot_option_def null_option_def)
  apply(case_tac "b", simp_all add: invalid_def bot_option_def)
  proof - fix r typeoid          let ?t = "(Some ((Some (r)))) \<in> (Some o OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>) ` (ran ((heap ((in_pre_state (\<tau>))))))"
          let ?sel_any = "(select_object_any\<^sub>S\<^sub>e\<^sub>t ((deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) (reconst_basetype))))" show "(select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss (?sel_any) (typeoid) (\<tau>)) = (Some ((Some (r)))) \<Longrightarrow> ?t"
  apply(case_tac "typeoid", simp add: select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n__boss_def)
  proof - fix opt show "(((case opt of None \<Rightarrow> null
    | (Some (x)) \<Rightarrow> ((?sel_any) (x)))) (\<tau>)) = (Some ((Some (r)))) \<Longrightarrow> ?t"
  apply(case_tac "opt", auto simp: null_fun_def null_option_def bot_option_def)
  proof - fix aa show "((?sel_any) (aa) (\<tau>)) = (Some ((Some (r)))) \<Longrightarrow> ?t" when "\<tau> \<Turnstile> (\<delta> (((?sel_any) (aa))))"
  apply(insert that, drule select_object_any_exec\<^sub>S\<^sub>e\<^sub>t[simplified foundation22], erule exE)
  proof - fix e show "?t" when "((?sel_any) (aa) (\<tau>)) = (Some ((Some (r))))" "((?sel_any) (aa) (\<tau>)) = (deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (in_pre_state) (reconst_basetype) (e) (\<tau>))"
  apply(insert that, simp add: deref_oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def)
  apply(case_tac "(heap ((in_pre_state (\<tau>))) (e))", simp add: invalid_def bot_option_def, simp)
  proof - fix aaa show "(case aaa of (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (obj)) \<Rightarrow> (reconst_basetype (obj) (\<tau>))
    | _ \<Rightarrow> (invalid (\<tau>))) = (Some ((Some (r)))) \<Longrightarrow> (heap ((in_pre_state (\<tau>))) (e)) = (Some (aaa)) \<Longrightarrow> ?t"
  apply(case_tac "aaa", auto simp: invalid_def bot_option_def image_def ran_def)
  apply(rule exI[where x = "(in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (r))"], simp add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>_def Let_def reconst_basetype_def split: if_split_asm)
by(rule) qed
  apply_end((blast)+)
 qed
  apply_end(simp add: foundation16 bot_option_def null_option_def)
 qed qed qed qed qed
  apply_end(simp_all)
 qed

(* 138 ************************************ 904 + 0 *)  (* term Floor1_access.print_access_repr_allinst *)

(* 139 ************************************ 904 + 1 *)
section \<open>Class Model: Towards the Object Instances\<close>

(* 140 ************************************ 905 + 1 *)
text \<open>

The example we are defining in this section comes from the \autoref{fig:Employee-DesignModel-UMLPart-generated-generatededm1_system-states}.
\<close>

(* 141 ************************************ 906 + 1 *)
text_raw \<open>
\begin{figure}
\includegraphics[width=\textwidth]{figures/pre-post.pdf}
\caption{(a) pre-state $\sigma_1$ and
  (b) post-state $\sigma_1'$.}
\label{fig:Employee-DesignModel-UMLPart-generated-generatededm1_system-states}
\end{figure}
\<close>

(* 142 ************************************ 907 + 1 *)
text \<open>\<close>

(* 143 ************************************ 908 + 1 *)
text_raw \<open>\<close>

(* 144 ************************************ 909 + 1 *)  (* term Floor1_examp.print_examp_def_st_defs *)
lemmas [simp,code_unfold] = state.defs
                            const_ss

(* 145 ************************************ 910 + 1 *)  (* term Floor1_astype.print_astype_lemmas_id2 *)
lemmas[simp,code_unfold] = OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Planet
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Galaxy
                            OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Galaxy
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_OclAny
                            OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_OclAny
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person
                            OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Planet
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Planet
                            OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Galaxy

(* 146 ************************************ 911 + 1 *)
section \<open>Instance\<close>

(* 147 ************************************ 912 + 2 *)  (* term Floor1_examp.print_examp_instance_defassoc_typecheck_var *)
definition "(typecheck_instance_bad_head_on_lhs_P1_X0_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 (P1) (X0) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1)) = ()"
definition "typecheck_instance_extra_variables_on_rhs_P1_X0_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 = (\<lambda>P1 X0 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1. (P1 , P1 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2))"

(* 148 ************************************ 914 + 12 *)  (* term Floor1_examp.print_examp_instance_defassoc *)
definition "oid1 = 1"
definition "oid2 = 2"
definition "oid3 = 3"
definition "oid4 = 4"
definition "oid5 = 5"
definition "oid6 = 6"
definition "oid7 = 7"
definition "oid8 = 8"
definition "oid9 = 9"
definition "oid10 = 10"
definition "oid11 = 11"
definition "inst_assoc1 = (\<lambda>oid_class to_from oid. ((case (deref_assocs_list ((to_from::oid list list \<Rightarrow> oid list \<times> oid list)) ((oid::oid)) ((the ((((map_of_list ([(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss , (List.map ((\<lambda>(x , y). [x , y]) o switch\<^sub>2_01) ([[[oid7] , [oid7]] , [[oid6] , [oid7]] , [[oid2] , [oid2]] , [[oid1] , [oid2]]])))]))) ((oid_class::oid))))))) of Nil \<Rightarrow> None
    | l \<Rightarrow> (Some (l)))::oid list option))"

(* 149 ************************************ 926 + 22 *)  (* term Floor1_examp.print_examp_instance *)
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid1) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid1))) (\<lfloor>1300\<rfloor>))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid2) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid2))) (\<lfloor>1800\<rfloor>))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid3) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid3))) (None))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid4) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid4))) (\<lfloor>2900\<rfloor>))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid5) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid5))) (\<lfloor>3500\<rfloor>))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid6) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid6))) (\<lfloor>2500\<rfloor>))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid7) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid7))) (\<lfloor>3200\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 = ((((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (inst_assoc1))\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y inst_assoc = (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y ((mk\<E>\<X>\<T>\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (oid8))))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8::\<cdot>OclAny) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid9) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid9))) (\<lfloor>0\<rfloor>))"
definition "(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "X0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid10) (None) (None) (None) (None) (\<lfloor>[[oid11]]\<rfloor>))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid10))) (None))"
definition "(X0::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(X0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc1))\<rfloor>\<rfloor>))"
definition "P1\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t inst_assoc = (mk\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t ((mk\<E>\<X>\<T>\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (oid11) (None) (None) (\<lfloor>[[oid11] , [oid11]]\<rfloor>))) (None) (None))"
definition "(P1::\<cdot>Planet) = ((\<lambda>_. \<lfloor>\<lfloor>(P1\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t (inst_assoc1))\<rfloor>\<rfloor>))"

(* 150 ************************************ 948 + 1 *)  (* term Floor1_examp.print_examp_instance_defassoc_typecheck *)
ML \<open>(Ty'.check ([(META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .boss \<cong> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 }") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .boss \<cong> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 }") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 /* unnamed attribute */ \<cong> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 }") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .boss \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .boss \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .boss \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .boss \<cong> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 }") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .boss \<cong> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 }") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 /* unnamed attribute */ \<cong> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 }") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .boss \<cong> Set{}") , (META.Writeln , "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "X0 .boss \<cong> Set{}") , (META.Writeln , "X0 /* unnamed attribute */ \<cong> Set{}")]) (" error(s)"))\<close>

(* 151 ************************************ 949 + 1 *)
section \<open>Instance\<close>

(* 152 ************************************ 950 + 2 *)  (* term Floor1_examp.print_examp_instance_defassoc_typecheck_var *)
definition "(typecheck_instance_bad_head_on_lhs_\<sigma>\<^sub>1_object4_\<sigma>\<^sub>1_object2_\<sigma>\<^sub>1_object1_\<sigma>\<^sub>1_object0 (\<sigma>\<^sub>1_object4) (\<sigma>\<^sub>1_object2) (\<sigma>\<^sub>1_object1) (\<sigma>\<^sub>1_object0)) = ()"
definition "typecheck_instance_extra_variables_on_rhs_\<sigma>\<^sub>1_object4_\<sigma>\<^sub>1_object2_\<sigma>\<^sub>1_object1_\<sigma>\<^sub>1_object0 = (\<lambda>\<sigma>\<^sub>1_object4 \<sigma>\<^sub>1_object2 \<sigma>\<^sub>1_object1 \<sigma>\<^sub>1_object0. (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1))"

(* 153 ************************************ 952 + 1 *)  (* term Floor1_examp.print_examp_instance_defassoc *)
definition "inst_assoc12 = (\<lambda>oid_class to_from oid. ((case (deref_assocs_list ((to_from::oid list list \<Rightarrow> oid list \<times> oid list)) ((oid::oid)) ((the ((((map_of_list ([(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss , (List.map ((\<lambda>(x , y). [x , y]) o switch\<^sub>2_01) ([[[oid6] , [oid4]] , [[oid4] , [oid5]] , [[oid1] , [oid2]]])))]))) ((oid_class::oid))))))) of Nil \<Rightarrow> None
    | l \<Rightarrow> (Some (l)))::oid list option))"

(* 154 ************************************ 953 + 8 *)  (* term Floor1_examp.print_examp_instance *)
definition "\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid1) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid1))) (\<lfloor>1000\<rfloor>))"
definition "(\<sigma>\<^sub>1_object0::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc12))\<rfloor>\<rfloor>))"
definition "\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid2) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid2))) (\<lfloor>1200\<rfloor>))"
definition "(\<sigma>\<^sub>1_object1::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc12))\<rfloor>\<rfloor>))"
definition "\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid4) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid4))) (\<lfloor>2600\<rfloor>))"
definition "(\<sigma>\<^sub>1_object2::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc12))\<rfloor>\<rfloor>))"
definition "\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n inst_assoc = (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n ((mk\<E>\<X>\<T>\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (oid6) (None) (None) (None) (None) (None))) (((inst_assoc) (oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss) (switch\<^sub>2_01) (oid6))) (\<lfloor>2300\<rfloor>))"
definition "(\<sigma>\<^sub>1_object4::\<cdot>Person) = ((\<lambda>_. \<lfloor>\<lfloor>(\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (inst_assoc12))\<rfloor>\<rfloor>))"

(* 155 ************************************ 961 + 1 *)  (* term Floor1_examp.print_examp_instance_defassoc_typecheck *)
ML \<open>(Ty'.check ([(META.Writeln , "\<sigma>\<^sub>1_object0 .boss \<cong> Set{ \<sigma>\<^sub>1_object1 }") , (META.Writeln , "\<sigma>\<^sub>1_object0 /* unnamed attribute */ \<cong> Set{}") , (META.Writeln , "\<sigma>\<^sub>1_object1 .boss \<cong> Set{}") , (META.Writeln , "\<sigma>\<^sub>1_object1 /* unnamed attribute */ \<cong> Set{ \<sigma>\<^sub>1_object0 }") , (META.Writeln , "\<sigma>\<^sub>1_object2 .boss \<cong> Set{ /*5*/ }") , (META.Writeln , "\<sigma>\<^sub>1_object2 /* unnamed attribute */ \<cong> Set{ \<sigma>\<^sub>1_object4 }") , (META.Writeln , "\<sigma>\<^sub>1_object4 .boss \<cong> Set{ \<sigma>\<^sub>1_object2 }") , (META.Writeln , "\<sigma>\<^sub>1_object4 /* unnamed attribute */ \<cong> Set{}")]) (" error(s)"))\<close>

(* 156 ************************************ 962 + 1 *)
section \<open>State (Floor 2)\<close>

(* 157 ************************************ 963 + 1 *)
locale state_\<sigma>\<^sub>1 =
fixes "oid1" :: "nat"
fixes "oid2" :: "nat"
fixes "oid4" :: "nat"
fixes "oid5" :: "nat"
fixes "oid6" :: "nat"
fixes "oid9" :: "nat"
assumes distinct_oid: "(distinct ([oid1 , oid2 , oid4 , oid5 , oid6 , oid9]))"
fixes "\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object0" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object0_def: "\<sigma>\<^sub>1_object0 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object1" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object1_def: "\<sigma>\<^sub>1_object1 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object2" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object2_def: "\<sigma>\<^sub>1_object2 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object4" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object4_def: "\<sigma>\<^sub>1_object4 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
begin
definition "\<sigma>\<^sub>1 = (state.make ((Map.empty (oid1 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid2 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid4 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid5 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid6 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid9 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))) ((map_of_list ([(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss , (List.map ((\<lambda>(x , y). [x , y]) o switch\<^sub>2_01) ([[[oid1] , [oid2]] , [[oid4] , [oid5]] , [[oid6] , [oid4]]])))]))))"

lemma dom_\<sigma>\<^sub>1 : "(dom ((heap (\<sigma>\<^sub>1)))) = {oid1 , oid2 , oid4 , oid5 , oid6 , oid9}"
by(auto simp: \<sigma>\<^sub>1_def)

lemmas[simp,code_unfold] = dom_\<sigma>\<^sub>1

lemma perm_\<sigma>\<^sub>1 : "\<sigma>\<^sub>1 = (state.make ((Map.empty (oid9 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid6 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid5 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid4 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid2 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid1 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))) ((assocs (\<sigma>\<^sub>1))))"
  apply(simp add: \<sigma>\<^sub>1_def)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (4) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (5) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (4) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
by(simp)

lemma \<sigma>\<^sub>1_OclAllInstances_generic_exec_Person :
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1)) \<Turnstile> (OclAllInstances_generic (pre_post) (Person)) \<doteq> Set{\<sigma>\<^sub>1_object0 , \<sigma>\<^sub>1_object1 , \<sigma>\<^sub>1_object2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 , \<sigma>\<^sub>1_object4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9}"
  apply(subst perm_\<sigma>\<^sub>1)
  apply(simp only: state.make_def \<sigma>\<^sub>1_object0_def \<sigma>\<^sub>1_object1_def \<sigma>\<^sub>1_object2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def \<sigma>\<^sub>1_object4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp, simp, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp, simp, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp, simp, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp, simp, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp, simp, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp, simp, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>_def)?)

lemma \<sigma>\<^sub>1_OclAllInstances_at_post_exec_Person :
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
shows "(st , \<sigma>\<^sub>1) \<Turnstile> (OclAllInstances_at_post (Person)) \<doteq> Set{\<sigma>\<^sub>1_object0 , \<sigma>\<^sub>1_object1 , \<sigma>\<^sub>1_object2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 , \<sigma>\<^sub>1_object4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_Person, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_at_pre_exec_Person :
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
shows "(\<sigma>\<^sub>1 , st) \<Turnstile> (OclAllInstances_at_pre (Person)) \<doteq> Set{\<sigma>\<^sub>1_object0 , \<sigma>\<^sub>1_object1 , \<sigma>\<^sub>1_object2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 , \<sigma>\<^sub>1_object4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_Person, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_generic_exec_Planet :
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1)) \<Turnstile> (OclAllInstances_generic (pre_post) (Planet)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(Planet) , \<sigma>\<^sub>1_object1 .oclAsType(Planet) , \<sigma>\<^sub>1_object2 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(Planet) , \<sigma>\<^sub>1_object4 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Planet)}"
  apply(subst perm_\<sigma>\<^sub>1)
  apply(simp only: state.make_def \<sigma>\<^sub>1_object0_def \<sigma>\<^sub>1_object1_def \<sigma>\<^sub>1_object2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def \<sigma>\<^sub>1_object4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA>_def)?)

lemma \<sigma>\<^sub>1_OclAllInstances_at_post_exec_Planet :
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
shows "(st , \<sigma>\<^sub>1) \<Turnstile> (OclAllInstances_at_post (Planet)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(Planet) , \<sigma>\<^sub>1_object1 .oclAsType(Planet) , \<sigma>\<^sub>1_object2 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(Planet) , \<sigma>\<^sub>1_object4 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Planet)}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_Planet, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_at_pre_exec_Planet :
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
shows "(\<sigma>\<^sub>1 , st) \<Turnstile> (OclAllInstances_at_pre (Planet)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(Planet) , \<sigma>\<^sub>1_object1 .oclAsType(Planet) , \<sigma>\<^sub>1_object2 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(Planet) , \<sigma>\<^sub>1_object4 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Planet)}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_Planet, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_generic_exec_Galaxy :
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1)) \<Turnstile> (OclAllInstances_generic (pre_post) (Galaxy)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object1 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object2 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object4 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Galaxy)}"
  apply(subst perm_\<sigma>\<^sub>1)
  apply(simp only: state.make_def \<sigma>\<^sub>1_object0_def \<sigma>\<^sub>1_object1_def \<sigma>\<^sub>1_object2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def \<sigma>\<^sub>1_object4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA>_def)?)

lemma \<sigma>\<^sub>1_OclAllInstances_at_post_exec_Galaxy :
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
shows "(st , \<sigma>\<^sub>1) \<Turnstile> (OclAllInstances_at_post (Galaxy)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object1 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object2 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object4 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Galaxy)}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_Galaxy, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_at_pre_exec_Galaxy :
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
shows "(\<sigma>\<^sub>1 , st) \<Turnstile> (OclAllInstances_at_pre (Galaxy)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object1 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object2 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(Galaxy) , \<sigma>\<^sub>1_object4 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Galaxy)}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_Galaxy, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_generic_exec_OclAny :
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1)) \<Turnstile> (OclAllInstances_generic (pre_post) (OclAny)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(OclAny) , \<sigma>\<^sub>1_object1 .oclAsType(OclAny) , \<sigma>\<^sub>1_object2 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny) , \<sigma>\<^sub>1_object4 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)}"
  apply(subst perm_\<sigma>\<^sub>1)
  apply(simp only: state.make_def \<sigma>\<^sub>1_object0_def \<sigma>\<^sub>1_object1_def \<sigma>\<^sub>1_object2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def \<sigma>\<^sub>1_object4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>_def)?)

lemma \<sigma>\<^sub>1_OclAllInstances_at_post_exec_OclAny :
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
shows "(st , \<sigma>\<^sub>1) \<Turnstile> (OclAllInstances_at_post (OclAny)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(OclAny) , \<sigma>\<^sub>1_object1 .oclAsType(OclAny) , \<sigma>\<^sub>1_object2 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny) , \<sigma>\<^sub>1_object4 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_OclAny, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1_OclAllInstances_at_pre_exec_OclAny :
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
shows "(\<sigma>\<^sub>1 , st) \<Turnstile> (OclAllInstances_at_pre (OclAny)) \<doteq> Set{\<sigma>\<^sub>1_object0 .oclAsType(OclAny) , \<sigma>\<^sub>1_object1 .oclAsType(OclAny) , \<sigma>\<^sub>1_object2 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny) , \<sigma>\<^sub>1_object4 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1_OclAllInstances_generic_exec_OclAny, simp_all only: assms, simp_all)

ML \<open>(Ty'.check ([]) (" error(s)"))\<close>
end

(* 158 ************************************ 964 + 1 *)  (* term Floor2_examp.print_examp_def_st_def_interp *)
definition "(state_interpretation_\<sigma>\<^sub>1 (\<tau>)) = (state_\<sigma>\<^sub>1 (oid1) (oid2) (oid4) (oid5) (oid6) (oid9) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object0 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object0) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object1 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object1) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object2 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object2) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object4 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object4) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"

(* 159 ************************************ 965 + 1 *)
section \<open>State (Floor 2)\<close>

(* 160 ************************************ 966 + 1 *)
locale state_\<sigma>\<^sub>1' =
fixes "oid1" :: "nat"
fixes "oid2" :: "nat"
fixes "oid3" :: "nat"
fixes "oid4" :: "nat"
fixes "oid6" :: "nat"
fixes "oid7" :: "nat"
fixes "oid8" :: "nat"
fixes "oid9" :: "nat"
assumes distinct_oid: "(distinct ([oid1 , oid2 , oid3 , oid4 , oid6 , oid7 , oid8 , oid9]))"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y" :: "ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7" :: "\<cdot>OclAny"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y" :: "ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8" :: "\<cdot>OclAny"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
begin
definition "\<sigma>\<^sub>1' = (state.make ((Map.empty (oid1 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid2 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid3 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid4 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid6 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid7 \<mapsto> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))) (oid8 \<mapsto> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))) (oid9 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))) ((map_of_list ([(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_0___boss , (List.map ((\<lambda>(x , y). [x , y]) o switch\<^sub>2_01) ([[[oid1] , [oid2]] , [[oid2] , [oid2]] , [[oid6] , [oid7]] , [[oid7] , [oid7]]])))]))))"

lemma dom_\<sigma>\<^sub>1' : "(dom ((heap (\<sigma>\<^sub>1')))) = {oid1 , oid2 , oid3 , oid4 , oid6 , oid7 , oid8 , oid9}"
by(auto simp: \<sigma>\<^sub>1'_def)

lemmas[simp,code_unfold] = dom_\<sigma>\<^sub>1'

lemma perm_\<sigma>\<^sub>1' : "\<sigma>\<^sub>1' = (state.make ((Map.empty (oid9 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid8 \<mapsto> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))) (oid7 \<mapsto> (in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))) (oid6 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid4 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid3 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid2 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))) (oid1 \<mapsto> (in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))) ((assocs (\<sigma>\<^sub>1'))))"
  apply(simp add: \<sigma>\<^sub>1'_def)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (4) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (5) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (4) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (6) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (5) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (4) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (7) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (6) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (5) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (4) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (3) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (2) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
  apply(subst (1) fun_upd_twist, metis distinct_oid distinct_length_2_or_more)
by(simp)

lemma \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Person :
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)::\<cdot>OclAny)) .oclAsType(Person))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1')) \<Turnstile> (OclAllInstances_generic (pre_post) (Person)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9}"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: state.make_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_ntc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp del: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>_def)?)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_post_exec_Person :
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)::\<cdot>OclAny)) .oclAsType(Person))"
shows "(st , \<sigma>\<^sub>1') \<Turnstile> (OclAllInstances_at_post (Person)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Person, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_pre_exec_Person :
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Person ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Person ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)::\<cdot>OclAny)) .oclAsType(Person))"
shows "(\<sigma>\<^sub>1' , st) \<Turnstile> (OclAllInstances_at_pre (Person)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Person, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Planet :
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Planet ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1')) \<Turnstile> (OclAllInstances_generic (pre_post) (Planet)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Planet)}"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: state.make_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_ntc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp)
  apply(subst state_update_vs_allInstances_generic_ntc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp del: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>P\<^sub>l\<^sub>a\<^sub>n\<^sub>e\<^sub>t_\<AA>_def)?)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_post_exec_Planet :
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Planet ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
shows "(st , \<sigma>\<^sub>1') \<Turnstile> (OclAllInstances_at_post (Planet)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Planet)}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Planet, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_pre_exec_Planet :
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Planet ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Planet ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Planet ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Planet))"
shows "(\<sigma>\<^sub>1' , st) \<Turnstile> (OclAllInstances_at_pre (Planet)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(Planet) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Planet)}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Planet, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Galaxy :
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Galaxy ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1')) \<Turnstile> (OclAllInstances_generic (pre_post) (Galaxy)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Galaxy)}"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: state.make_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_ntc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp)
  apply(subst state_update_vs_allInstances_generic_ntc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp del: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>G\<^sub>a\<^sub>l\<^sub>a\<^sub>x\<^sub>y_\<AA>_def)?)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_post_exec_Galaxy :
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Galaxy ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
shows "(st , \<sigma>\<^sub>1') \<Turnstile> (OclAllInstances_at_post (Galaxy)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Galaxy)}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Galaxy, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_pre_exec_Galaxy :
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(Galaxy ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Galaxy ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = None"
assumes [simp]: "(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
assumes [simp]: "(\<lambda>_. \<lfloor>(Galaxy ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(Galaxy))"
shows "(\<sigma>\<^sub>1' , st) \<Turnstile> (OclAllInstances_at_pre (Galaxy)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(Galaxy) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(Galaxy)}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_Galaxy, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_generic_exec_OclAny :
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<And>a. (pre_post ((mk (a)))) = a)"
shows "(mk (\<sigma>\<^sub>1')) \<Turnstile> (OclAllInstances_generic (pre_post) (OclAny)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)}"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: state.make_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(subst state_update_vs_allInstances_generic_tc, simp, simp, (metis distinct_oid distinct_length_2_or_more)?, simp only: assms, blast, simp, rule const_StrictRefEq\<^sub>S\<^sub>e\<^sub>t_including, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp del: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person, simp, rule OclIncluding_cong, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def, (simp only: assms[symmetric ])?, simp add: valid_def OclValid_def bot_fun_def bot_option_def)
  apply(rule state_update_vs_allInstances_generic_empty)
by(simp_all only: assms, (simp_all add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_\<AA>_def)?)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_post_exec_OclAny :
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
shows "(st , \<sigma>\<^sub>1') \<Turnstile> (OclAllInstances_at_post (OclAny)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)}"
  unfolding OclAllInstances_at_post_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_OclAny, simp_all only: assms, simp_all)

lemma \<sigma>\<^sub>1'_OclAllInstances_at_pre_exec_OclAny :
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) \<noteq> None"
assumes [simp]: "(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) \<noteq> None"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
assumes [simp]: "(\<lambda>_. \<lfloor>(OclAny ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n))))\<rfloor>) = ((((\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)::\<cdot>Person)) .oclAsType(OclAny))"
shows "(\<sigma>\<^sub>1' , st) \<Turnstile> (OclAllInstances_at_pre (OclAny)) \<doteq> Set{X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny) , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)}"
  unfolding OclAllInstances_at_pre_def
by(rule \<sigma>\<^sub>1'_OclAllInstances_generic_exec_OclAny, simp_all only: assms, simp_all)

ML \<open>(Ty'.check ([]) (" error(s)"))\<close>
end

(* 161 ************************************ 967 + 1 *)  (* term Floor2_examp.print_examp_def_st_def_interp *)
definition "(state_interpretation_\<sigma>\<^sub>1' (\<tau>)) = (state_\<sigma>\<^sub>1' (oid1) (oid2) (oid3) (oid4) (oid6) (oid7) (oid8) (oid9) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"

(* 162 ************************************ 968 + 1 *)
section \<open>Transition (Floor 2)\<close>

(* 163 ************************************ 969 + 1 *)
locale transition_\<sigma>\<^sub>1_\<sigma>\<^sub>1' =
fixes "oid1" :: "nat"
fixes "oid2" :: "nat"
fixes "oid3" :: "nat"
fixes "oid4" :: "nat"
fixes "oid5" :: "nat"
fixes "oid6" :: "nat"
fixes "oid7" :: "nat"
fixes "oid8" :: "nat"
fixes "oid9" :: "nat"
assumes distinct_oid: "(distinct ([oid1 , oid2 , oid3 , oid4 , oid5 , oid6 , oid7 , oid8 , oid9]))"
fixes "\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object0" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object0_def: "\<sigma>\<^sub>1_object0 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object1" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object1_def: "\<sigma>\<^sub>1_object1 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object2" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object2_def: "\<sigma>\<^sub>1_object2 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "\<sigma>\<^sub>1_object4" :: "\<cdot>Person"
assumes \<sigma>\<^sub>1_object4_def: "\<sigma>\<^sub>1_object4 = (\<lambda>_. \<lfloor>\<lfloor>\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y" :: "ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7" :: "\<cdot>OclAny"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y" :: "ty\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8" :: "\<cdot>OclAny"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<rfloor>\<rfloor>)"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" :: "ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n"
fixes "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9" :: "\<cdot>Person"
assumes X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def: "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 = (\<lambda>_. \<lfloor>\<lfloor>X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<rfloor>\<rfloor>)"

assumes \<sigma>\<^sub>1: "(state_\<sigma>\<^sub>1 (oid1) (oid2) (oid4) (oid5) (oid6) (oid9) (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (\<sigma>\<^sub>1_object0) (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (\<sigma>\<^sub>1_object1) (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (\<sigma>\<^sub>1_object2) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5) (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (\<sigma>\<^sub>1_object4) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"

assumes \<sigma>\<^sub>1': "(state_\<sigma>\<^sub>1' (oid1) (oid2) (oid3) (oid4) (oid6) (oid7) (oid8) (oid9) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"
begin
interpretation state_\<sigma>\<^sub>1: state_\<sigma>\<^sub>1 "oid1" "oid2" "oid4" "oid5" "oid6" "oid9" "\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "\<sigma>\<^sub>1_object0" "\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "\<sigma>\<^sub>1_object1" "\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "\<sigma>\<^sub>1_object2" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5" "\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "\<sigma>\<^sub>1_object4" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9"
by(rule \<sigma>\<^sub>1)

interpretation state_\<sigma>\<^sub>1': state_\<sigma>\<^sub>1' "oid1" "oid2" "oid3" "oid4" "oid6" "oid7" "oid8" "oid9" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n" "X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9"
by(rule \<sigma>\<^sub>1')

definition "\<sigma>\<^sub>1 = state_\<sigma>\<^sub>1.\<sigma>\<^sub>1"

definition "\<sigma>\<^sub>1' = state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'"

lemma basic_\<sigma>\<^sub>1_\<sigma>\<^sub>1'_wff :
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid1"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid1"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid2"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid2"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid3"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid4"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid4"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid5"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid6"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid6"
assumes [simp]: "(oid_of ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = oid7"
assumes [simp]: "(oid_of ((in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)))) = oid8"
assumes [simp]: "(oid_of ((in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)))) = oid9"
shows "(WFF ((state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1')))"
  proof - have [simp]: "oid1 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid1 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid2 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid3 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid4 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid5 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid6 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid7 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid8 \<noteq> oid9" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid1" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid2" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid3" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid4" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid5" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid6" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid7" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
  proof - have [simp]: "oid9 \<noteq> oid8" by(metis distinct_oid distinct_length_2_or_more) show ?thesis
by(auto simp: WFF_def state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def) qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed qed

lemma oid1\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1_OclIsMaintained :
assumes [simp]: "(oid_of (\<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid1"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (\<sigma>\<^sub>1_object0))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def \<sigma>\<^sub>1_object0_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid1\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsMaintained :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid1"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid2\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1_OclIsMaintained :
assumes [simp]: "(oid_of (\<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid2"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (\<sigma>\<^sub>1_object1))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def \<sigma>\<^sub>1_object1_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid2\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsMaintained :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid2"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid3\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsNew :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid3"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsNew (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def OclIsNew_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid4\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1_OclIsMaintained :
assumes [simp]: "(oid_of (\<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid4"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (\<sigma>\<^sub>1_object2))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def \<sigma>\<^sub>1_object2_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid4\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsMaintained :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid4"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid5\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1_OclIsDeleted :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid5"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsDeleted (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def OclIsDeleted_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid6\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1_OclIsMaintained :
assumes [simp]: "(oid_of (\<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid6"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (\<sigma>\<^sub>1_object4))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def \<sigma>\<^sub>1_object4_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid6\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsMaintained :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid6"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid7\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsNew :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)) = oid7"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsNew (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_def OclIsNew_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid8\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsNew :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y)) = oid8"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsNew (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_def OclIsNew_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid9\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1_OclIsMaintained :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid9"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)

lemma oid9\<sigma>\<^sub>1\<sigma>\<^sub>1'_\<sigma>\<^sub>1'_OclIsMaintained :
assumes [simp]: "(oid_of (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)) = oid9"
shows "(state_\<sigma>\<^sub>1.\<sigma>\<^sub>1 , state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1') \<Turnstile> (OclIsMaintained (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"
  apply(simp add: state_\<sigma>\<^sub>1.\<sigma>\<^sub>1_def state_\<sigma>\<^sub>1'.\<sigma>\<^sub>1'_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def OclIsMaintained_def OclValid_def oid_of_option_def)
by((metis distinct_oid distinct_length_2_or_more)?)
end

(* 164 ************************************ 970 + 1 *)  (* term Floor2_examp.print_transition_def_interp *)
definition "(pp_\<sigma>\<^sub>1_\<sigma>\<^sub>1' (\<tau>)) = (transition_\<sigma>\<^sub>1_\<sigma>\<^sub>1' (oid1) (oid2) (oid3) (oid4) (oid5) (oid6) (oid7) (oid8) (oid9) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object0 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object0) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object1 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object1) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object2 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object2) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5) (\<lceil>\<lceil>(\<sigma>\<^sub>1_object4 (\<tau>))\<rceil>\<rceil>) (\<sigma>\<^sub>1_object4) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8) (\<lceil>\<lceil>(X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 (\<tau>))\<rceil>\<rceil>) (X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9))"

(* 165 ************************************ 971 + 3 *)  (* term Floor2_examp.print_transition_lemmas_oid *)
lemmas pp_oid_\<sigma>\<^sub>1_\<sigma>\<^sub>1' = oid1_def
                            oid2_def
                            oid3_def
                            oid4_def
                            oid5_def
                            oid6_def
                            oid7_def
                            oid8_def
                            oid9_def
lemmas pp_object_\<sigma>\<^sub>1_\<sigma>\<^sub>1' = \<sigma>\<^sub>1_object0_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def
                            \<sigma>\<^sub>1_object1_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def
                            \<sigma>\<^sub>1_object2_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5_def
                            \<sigma>\<^sub>1_object4_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9_def
lemmas pp_object_ty_\<sigma>\<^sub>1_\<sigma>\<^sub>1' = \<sigma>\<^sub>1_object0\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            \<sigma>\<^sub>1_object1\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            \<sigma>\<^sub>1_object2\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            \<sigma>\<^sub>1_object4\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_def
                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_def

(* 166 ************************************ 974 + 1 *)
section \<open>Context (Floor 2)\<close>

(* 167 ************************************ 975 + 6 *)  (* term Floor2_ctxt.print_ctxt_pre_post *)
axiomatization where dot__contents_Person_def:
"(self::\<cdot>Person) .contents() \<equiv> (\<lambda>\<tau>. (Eps ((\<lambda>result. (HOL.Let ((\<lambda>_. result)) ((\<lambda>result. (if ((\<tau> \<Turnstile> ((\<delta> (self))))) then (\<tau> \<Turnstile> ((((UML_Logic.false :: (((_, Product_Type.unit) UML_Types.state.state_ext \<times> (_, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option)))))) \<and> (\<tau> \<Turnstile> ((((((UML_Logic.StrongEq :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (result)) (((((UML_Logic.OclIf :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e)))))) ((((UML_Logic.StrictRefEq :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot_0___boss :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))) (self))) ((UML_Types.null_class.null :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option))))) ((((UML_Set.OclIncluding :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e))))) ((UML_Set.mtSet :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e)))) (((Employee_DesignModel_UMLPart_generated.dot__salary :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (self)))) ((((UML_Set.OclIncluding :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e))))) (((Employee_DesignModel_UMLPart_generated.dot__contents :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> (((Int.int) Option.option) Option.option) UML_Types.Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e)))) (((Employee_DesignModel_UMLPart_generated.dot_0___boss :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))) (self)))) (((Employee_DesignModel_UMLPart_generated.dot__salary :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (self)))) and (UML_Logic.true :: (((_, Product_Type.unit) UML_Types.state.state_ext \<times> (_, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option)))))) else (\<tau> \<Turnstile> (result \<triangleq> invalid))))))))))"
thm dot__contents_Person_def
overloading dot__contents \<equiv> "(dot__contents::(\<cdot>Planet) \<Rightarrow> _)"
begin
  definition dot__contents_Planet : "(x::\<cdot>Planet) .contents() \<equiv> x .oclAsType(Person) .contents()"
end
overloading dot__contents \<equiv> "(dot__contents::(\<cdot>Galaxy) \<Rightarrow> _)"
begin
  definition dot__contents_Galaxy : "(x::\<cdot>Galaxy) .contents() \<equiv> x .oclAsType(Person) .contents()"
end
overloading dot__contents \<equiv> "(dot__contents::(\<cdot>OclAny) \<Rightarrow> _)"
begin
  definition dot__contents_OclAny : "(x::\<cdot>OclAny) .contents() \<equiv> x .oclAsType(Person) .contents()"
end
ML \<open>(Ty'.check ([]) (" error(s)"))\<close>

(* 168 ************************************ 981 + 0 *)  (* term Floor2_ctxt.print_ctxt_inv *)

(* 169 ************************************ 981 + 0 *)  (* term Floor2_ctxt.print_ctxt_thm *)

(* 170 ************************************ 981 + 1 *)
section \<open>Context (Floor 2)\<close>

(* 171 ************************************ 982 + 0 *)  (* term Floor2_ctxt.print_ctxt_pre_post *)

(* 172 ************************************ 982 + 3 *)  (* term Floor2_ctxt.print_ctxt_inv *)
definition "Person_aat_pre = (\<lambda>\<tau>. (\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Person))) ((\<lambda>self. (((UML_Logic.OclImplies :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((UML_Logic.OclNot :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option)))) ((((UML_Logic.StrictRefEq :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot_0___bossat_pre :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))) (self))) ((UML_Types.null_class.null :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))))) ((((UML_Logic.StrongEq :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot__salaryat_pre :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (self))) (((Employee_DesignModel_UMLPart_generated.dot__salaryat_pre :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (((Employee_DesignModel_UMLPart_generated.dot_0___bossat_pre :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))) (self)))))))))"
definition "Person_a = (\<lambda>\<tau>. (\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Person))) ((\<lambda>self. (((UML_Logic.OclImplies :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((UML_Logic.OclNot :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option)))) ((((UML_Logic.StrictRefEq :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot_0___boss :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))) (self))) ((UML_Types.null_class.null :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))))) ((((UML_Logic.StrongEq :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot__salary :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (self))) (((Employee_DesignModel_UMLPart_generated.dot__salary :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (((Employee_DesignModel_UMLPart_generated.dot_0___boss :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Employee_DesignModel_UMLPart_generated.ty\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n) Option.option) Option.option)))) (self)))))))))"
ML \<open>(Ty'.check ([]) (" error(s)"))\<close>

(* 173 ************************************ 985 + 1 *)  (* term Floor2_ctxt.print_ctxt_thm *)
thm Person_aat_pre_def Person_a_def

(* 174 ************************************ 986 + 1 *)
section \<open>Context (Floor 2)\<close>

(* 175 ************************************ 987 + 0 *)  (* term Floor2_ctxt.print_ctxt_pre_post *)

(* 176 ************************************ 987 + 3 *)  (* term Floor2_ctxt.print_ctxt_inv *)
definition "Planet_Aat_pre = (\<lambda>\<tau>. (\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_pre (Planet))) ((\<lambda>self. (((UML_Logic.OclAnd :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) ((UML_Logic.true :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option)))) ((((UML_Integer.OclLe\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot__weightat_pre :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (self))) ((UML_Integer.OclInt0 :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))))))))"
definition "Planet_A = (\<lambda>\<tau>. (\<tau> \<Turnstile> (UML_Set.OclForall ((OclAllInstances_at_post (Planet))) ((\<lambda>self. (((UML_Logic.OclAnd :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) ((UML_Logic.true :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option)))) ((((UML_Integer.OclLe\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((HOL.bool) Option.option) Option.option))))) (((Employee_DesignModel_UMLPart_generated.dot__weight :: ((((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> _) \<Rightarrow> (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))) (self))) ((UML_Integer.OclInt0 :: (((Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext \<times> (Employee_DesignModel_UMLPart_generated.\<AA>, Product_Type.unit) UML_Types.state.state_ext) \<Rightarrow> ((Int.int) Option.option) Option.option)))))))))"
ML \<open>(Ty'.check ([]) (" error(s)"))\<close>

(* 177 ************************************ 990 + 1 *)  (* term Floor2_ctxt.print_ctxt_thm *)
thm Planet_Aat_pre_def Planet_A_def

end